In the news today are speculations that the TTIP negotiations are in trouble. TTIP is the attempt to negotiate a near-to-free trade agreement between the EU and the USA. It is already well behind schedule and has come in for a lot of criticism from those who believe it will undermine consumer protection and increase the power of multinational corporation vis-a-vis governments.
Also in the news is the likelihood that due to an intervention by the European Commission the American computer giant Apple may be faced with billions of euros of back taxes that it did not know it was going to have to pay. A deal between the Irish government and Apple was, apparently, illegal under European law. This is also, of course, a rebuff for the Irish government. It also underlines the fact that those who, in the Brexit debate, argued that UK would be able to do deals with separate EU governments were wrong. All trade deals with the EU are with the EU as a whole.
The gradually increasing power of central EU authorities may be sometimes resented by member states, but it does tend to make the EU more powerful vis-a-vis non-EU countries. Where this tells most significantly is in dealing with the USA. In fact, it is arguable that the EU is actually the only country or bloc in the world that can be reasonable confident of winning confrontations with the USA over non-military issues.
When it comes to military matters, the US remains supreme and only Russia comes any where near to being able to flout it. However, some of the candidates in the coming US election have cast doubts upon the value or functioning of NATO and it must be the case that if EU-US relations were to deteriorate further and inevitable knock on effect would be that the EU would start to take on funding its own 'defence' requirements - in other words, rearming. Europe has an equivalent level of technology to the US and so could if it chose to spend the money, match it militarily at some time in the future.
Whether such a development is good for the world or conducive to world peace or not has to be an open question, but it may be the natural result of an inexorable process and small matters like a few billion euro in back taxes may simply be a small symptom of a bigger historical process.
The Apple affair may not dent Apple itself too much but it will register in US-EU relations. It will be interesting to see where the EU stands in relation to the Russo-Turkish advance in Syria. I imagine that the US will protest and Europe will remain neutral, keeping itself balanced between the two camps. The position of Turkey is interesting in relation to all this since it is a NATO member, has an application to join the EU in the distant future on the table, but is actually acting in concert with Russia. All of this changes the balance in the world by small degrees.