The thing about big and small states is a cyclic one imo, you have big empires/nations that conglomerate loads of smaller ones, that grow and become bigger and eventually rot and disintegrate into smaller components. The bigger a nation is, the harder it is for people to agree, and nationalism (meant as in the preference for your immediate surrounding area, be it a region, country or whatever it happens to be called at the time) has and will always be a big obstacle towards bigger entities, which works for companies because it is a pyramidal system, but cannot work for countries with democracy because you won't get people to agree on most things.
Another point that the EU has done is bringing countries that had historically been at odds with each other in common. I am not sure about this, but before 1945 I don't think there has been a period longer than 30-40 years without wars between the major states of western Europe, and by trading instead of invading, the EU is trying to help with that.
Also about the regions that are trying to split (Scotland and Catalonia I know something about, there may be more), they are attempting to split from the current state to attempt to join the EU with the status of member state, instead of just part of one, so it is not entirely towards splitting.