somebloke
The EU ended up incorporating the European Coal & Steel Community, EURATOM and the Western European Union (as well as other minor bodies). So as the current body that incorporates all of those historical groupings there really isn't any other way to present an award.
If you think about when some long-lived band is given a Lifetime Achievement Award, it's the current members who step up to receive the award even if early or founder members are long dead (and/or their best days are long behind them). I've never heard anyone begrudging such an award to The Rolling Stones, Fleetwood Mac etc in the same way that some are so begrudging to the EU.
As I said earlier, NATO aren't really deserving of a peace award - principally because it has proved incapable of stopping individual members from waging war. Its only benefit for peace within Europe has been the integration of procedure and equipment (common aircraft signalling, standardised ammunition, integration of command structures etc) as well as constant joint exercises and officer exchanges that means senior officers between nations view each other as colleagues and not rivals or potential enemies.
I actually think that it's a factor - it's like an oil that makes the wheels move more easily. But for the military only, unlike the various EU bodies that provide a similar service in trade, standards, resource allocation, research, economics, infrastructure, education et cetera. In this sense, NATO and the EU aren't really that different in the services they offer as supranational bodies (except that the EU has more democratic controls than NATO). And whilst I respect the position of people who oppose both of these supranational bodies from a political philosophy that opposes any pooling of sovereignty, as far as I'm concerned anyone who supports membership of NATO whilst opposing membership of the EU is quite clearly fucking insane.
Anyway - NATO. The main idea that people have about their role of providing peace in Europe is solely down to NATO protecting us from the Warsaw Pact, which is riven with 1950s-era US groupthink - not everyone in Europe actually bought into it, and documents uncovered after 1989 show that the Warsaw Pact's planning was primarily based around responding to NATO 'first strike' interventions. Obviously, it could then be argued that an absence of NATO would have made invasion more likely but then we're back into the Alice In Wonderland supposition that FlatPackHamster loves so much.
As for the point about democracies - that's true. But countries were only allowed in the EEC/EC/EU if they became democracies and could prove they were politically robust enough to stay democracies (Spain and Portugal weren't admitted following the end of their respective dictatorships until they could do this). Democracy becomes not just an end point but a means to an end, and the EU offered a lot of support and assistance to the Eastern European nations and some former Soviet republics post-1989 in transforming from authoritarian regimes to stable democracies. It's instructive to see how those republics who are more involved with Russia than the EU are a lot less stable and free than those that are.