I can't speak to the tactical differences between US and EU armies at the time.
On the first question, there have been lots of forum posts about this on other boards (a quick google search will reveal dozens) and the quick answer is....there's no way to really know. Numbers of army size from that time are general at best (the Union Army boasts over 600,000 soldiers at the end of the war, but how many of those were actual fighting men is anyone's guess - guessing various European army sizes might be even harder), looking at training vs experience in the various armies is going to be even harder, as is comparing general officer ability, and arguably the easiest thing to compare, technology of weapons, hits a snag when you realize you'd also have to try and figure out what sort of production output a country could reasonably sustain during a prolonged conflict (it seems clear to me that any European country would have to import massive amounts of raw materials to try and keep up with what the Union could produce by war's end).
So, this is a question that will never be satisfactorily answered in a way that will ever convince anyone to change their position on it....unless someone makes a mod for this game that lets us sim it out =P