i think the inefficiency and bureaucratic mess that is the eu is actually what prevents conflict between the eu countries, i think you are correct though that in its current form its unable to project power, and that leaves them to fall under the russian or us boot, but i dont see how a real unity of such diverse countries can come to be, it seems more likely that one country could become the dominant power in europe, and then the other eu countries would fall under their boot. maybe that is what many europeans would prefer, but if there becomes more than one power center and it would be effective it seems too likely it could lead to a larger conflict.  i think the eu system as it stands has been very effective at preventing war and large conflict between eu countries, but i think europeans shouldnt be naive that under a different system they could quickly fall back into conflict.
Russian Federation