Definition of Competition Policy: "government policy which tries to encourage competition by keeping a check on potential monopolies and making sure that businesses act fairly in relationship to each other." 
Strong cooperation between the US and the EU in implementation of competition policy has been a very successful venture in the US - EU relationship. Despite different underlying philosophies, methods and analytical techniques the last 10 years of cooperation resulted in significant improvements in measures of competition policy that affect both sides of the Atlantics. However, some say, in the nearest future US and EU competition leadership might experience serious challenges like a fight for recourses and competition for international influence and recognition (the drive to be seen as the global leader).
Bibliography: source 1
Nevertheless the US - EU rivalry aimed in constructive directions can have very useful results. A competition to exercise superior modern methods and implementation techniques is a competition people are better off having.
Now let's take a look at main current trends between US and EU competition policies: are they converging or diverging? What are the differences and similarities?
2. Why are the difference/similarities important?
There are at least three reasons nowadays why the differences/similarities or convergence/divergence in the direction of US-EU competition policies might have economic and political significance.
"First reason is that there is a high and growing level of interdependence between the regulatory policies of the two jurisdictions." In several areas of regulatory policy, the jurisdiction with the most intervention-intended strategy has power to set a global standard. There are very few (if any) multinational companies that do not operate in the European Union or in the United States. For cases like cartels, abuse of dominance or mergers, company's behavior must correspond to the standards and norms of the maximum limiting major jurisdictions with competition policy. In any case, the EU and the US are major jurisdictions - "major" in the meaning of having the proper authority and ability to enforce firms to follow their demands, standards and expectations.
Bibliography: source 1
"The second reason is connected to the process of enforcement." Even when the EU and US apply similar (or the same) standards and achieve the same assessment of the same market practice, differences in the process of investigation and agency decision-making can inflict costs on affected enterprises. If they try to achieve simpler, more common procedures, the EU and the US agencies can reduce the cost of executing transactions without any reduction in the quality of their substantial analysis.
Bibliography: sources 1; 2
"The third reason relates to introduction of new competition systems in the world." The US and the EU employ a large amount of resources on practical assistance of new competition policy systems and of countries trying to implement new competition laws. Somewhat 70 plus states that have established new competition laws in the past 3 decades have civil law systems. Many and most of those newly adopted systems often rely on an "administrative enforcement model" that matches the EU regime. To compare, very few emerging countries have adopted competition systems that follow the "adversarial prosecution model" applied by the US Department of Justice. Since the European institutional system is more comparable with the institutional platforms in most civil law countries, many emerging economies have a tendency to take a look first to EU models in designing and adopting their competition systems. This means that EU norms tend to be more steadily installed into the new competition policy regimes than US norms.
Bibliography: source 1
To sum up, the three background reasons for importance of differences and similarities between US and EU competition policies are: high and growing level of interdependence, enforcing process and new competition systems.
3. Differences and Similarities between two Systems
There is an often-stated view of EU and US competition executives that the common trend of competition policy in two jurisdictions has been in the direction of mutual acceptance of fundamental standards and the underlying concepts that support the implementation of those standards. If we take a look at general goals and certain areas of activity, we can clarify that opinion and highlight the noteworthy differences. Let's do it!
3.1 Structure of competition policy
The overall trend of EU and US competition laws in the past twenty years has been towards a decreasing gap regarding the proper focus of government enforcement and the application of litigation and non-litigation policy instruments.
3.2.1. Substantive Similarities
European Union has emerged as a strong partner of the United States in fighting cartels. Already by the beginning of 2002 the EU alone did fifteen decisions against setting prices and cartels that share the market, taking fines in excess of 2 billion Euros towards 60 and even more companies.
Both the EU and the US treat cartels in a rather negative way. EU and US officials today represent cartels as the most serious type of anticompetitive behavior, and both institutions have given substantial effort to chasing offenders and to generating new strategies for detecting secret arrangements. It is common now in both jurisdictions to increase punishments for violators. Two of the EU member states (Ireland and the United Kingdom) have adopted policies, like that of the DOJ (Department of Justice), of seeking punishment for individual offenders. There is an on-going debate within the European Commission and in the member states about the willingness to rely more on criminal sanctions. "This is an area in which EU practice in the past decade has converged substantially upon US norms by a process of voluntarily opting in."  Cartel fight is one of the great example where the EU adopted techniques (like leniency) that had been experimented extensively in the US.
Bibliography: source 1;6
In case of mergers Washington and Brussels have developed an excellent cooperative relationship in reviewing the growing number of mergers that are notified in both jurisdictions. This strong working relationship has helped to boost quite a degree of substantive convergence, particularly in terms of how we define markets and how we evaluate the competitive effects of horizontal mergers. As a result neither of jurisdictions had prohibited a merger over the other one's objection, disregarding some special cases.
Bibliography: source 2
The laws towards horizontal mergers in the EU and the US represent a significant degree of similarity. "Merger decisions by the courts of both jurisdictions - notably, Air Tours in the EU and Arch Coal, Giant/Western, SunGard and Whole Foods in the US - have tended to press EU and US enforcement authorities to satisfy more demanding standards and withstand closer judicial research of proof offered to demonstrate likely anticompetitive effects."  "Air Tours and Arch"Coal are similar in insisting on prosecutors to show what the cooperation among firms will result in after the merger is completed.
Bibliography: source 1;2
State Intervention in the Economy
Competition laws in the EU and the US reflect a growing awareness of how different forms of government intervention can hinder competition. Statements of the enforcement agencies in both jurisdictions show that both EU and the US treat government-issued barriers to rivalry as serious constraints to competition. Even though EU and US executive officials share suspicion of government restrictions to competitive market, the EU system sets a stronger platform to concern such restrictions. The US does not support the "state supports" portfolio of the EU. However, due to the mutual disbelief of EU and US officials toward a state intervention in competitive trade, this point can be considered as a point of potential similarity.
Bibliography: source 1;6
The stronger legal platform available in the EU, and the presence of the Parker immunity in the US, this area as well could have been included in the Substantive Dissimilarity section below.
3.2.2. Substantive Differences
Abuse of Dominance
To certain extent, the formal legal texts of the EU and the US create a fundament for differences in the attitudes towards the dominant firm. By their own means and by judicial interpretation, the US antitrust laws have no competitor to in spreading pricing prohibition. The US enforcement agencies have not pushed its excessive pricing authority to Europe, but the EU member states have shown a greater willingness to apply this measure under their own competition laws. US courts tend to say that court rooms and execution agencies make bigger mistakes by enforcing too hard rather than too little. This prospect does not appear in EU law enforcement or in statements by European enforcement officials.
Bibliography: source 2; 1; 3
"In their attitude, modern US Supreme Court decisions in cases such as Brooke Group, Trinko and Weyerhaeuser have shown greater carelessness in the direction of abuse of dominance, not like judicial decisions carried out in matters such as France Telecom/Wanadoo, Michelin II and British Airways." (Bibliography: source 1). EU decisions in IMS Health and Microsoft demonstrate a greater trend to negatively accuse refusals to deal than modern US decisions such as of Trinko. A case of abuse of dominance can occur in the EU at around 30-40 percent market share or below, while the US attack on attempted monopolizations usually concern market shares below 50 percent.
Bibliography: source 1
An important question for US and EU is how much the standards oriented on the effects will become the common foundation for better understanding of abuse of dominance issues. The EU prime paper on dominance and statements of EU officials express receptivity a greater reliance on an effects test and on reduced focus on the category-based assessment ( in cases such as British Airways). If broad EU/US agreements in general concepts take place, the question of application their application will remain.
Bibliography: source 1
220.127.116.11. Vertical Mergers
If we compare US and EU competition laws we can see that European Union creates a much more profound opportunities for intervening various conglomerate and vertical transactions. Even if to take a look at the late 2000's it is obvious that Europe has performed much better in way of defining and persecuting vertical mergers. There are some dissuading rumors about how expansively these possibilities are and will be exercised. The decision of the CFI (US) regarding Tetra Laval and GE - Honeywell proves that the commission has actually failed to supply proper evidence to prove a violation. At least decisions like this let us know that the American Commission will be obliged to satisfy quite demanding standards when challenging a conglomerate merger.
Bibliography: source 5
There are some significant differences in the policies of the United States and European Union. However they are involved not only in their own two-sided affairs but also in enormous number of issues with the rest of the world: regional initiatives, agreements and participation in international institutions like ICS or OECD. The US and EU are most commonly acting as partners in most of their international ventures and from year to year they must agree on their roles in each venture. Both sides know that successful participation in all those activities will be available only through a high quality job and therefore at a high cost. There is no point in trying to do those things cheap.
The problem is that United States, the EU and other entities around the world might find the transnational system of relationships as a burden. Therefore the main goal of two sides of the Atlantic as well as of the rest of the world will be related to the allocation of resources, individually and commonly. In this case, EU and the US might consider their mutual relationship as the most valuable thing and their top priority. This can be proved by the importance of the control of transatlantic commerce and by the fact that very often the US and the EU have mutual interests and strategies due to their large history of experiences. Moreover, the EU/US relationship has served, in effect, as a bilateral test bed for substantive concepts and processes that can be rolled out in a larger multinational setting. This mutual experience of both jurisdictions gives leaders of the Third World knowledge of what might be the proper and successful accomplishments in their common ventures around the globe. As two jurisdictions consider the limits of how much they can give up for the growing amount of mutual interests in international initiatives the new competition policy group of countries will need to generate a view of what the US and EU should do to help build a new healthy foundation around the world for strong and profound competition policy in the future.