North America, clearly. The US could just use that orbital missile defense system from CoD to blow up Europe and the rest of the world if they wanted.

The US would win easily and it wouldn't even need Canada and Mexico

Most armies here in Europe are understaffed are completely broken when it comes to vehicules. US has more and more capable warships/carriers than all Europe combined and their air force would win air superiority in a flash (not to mention we don't have stealth aircraft).

EU just by the number of soldiers, nukes wouldn't be used since both sides have them at great numbers

I'm pretty sure both sides have enough non-nuclear cruise/guided missiles to annihilate most major forces and bases the opponent has, so in my opinion it's all about who has better spotting/targeting, which should put NA at a good advantage.

The Navy of the European countries isn't up to the Navy of the US, so in a 1 on 1 war, it would have to defend. But in a 2 fronts war, the US would have to split its Navy in 2 groups, Pacific and Atlantic, and in that scenario the Navy of Europe could take a more agressive role.

In my opinion, th US would win because their army would all be under 1 command, avoiding a lot of the confusion that would reign over the European armies, but also because despite what they could say, they would use atomic bombs if they think it's worth it.

The combined military forces of Europe far outnumber the combined forces of North America. I don't think NA would stand a chance really, especially when you start to look at the European Special forces.

Here's some numbers; https://en.wikipedia.org/wiki/List_of_countries_by_number_of_troops

I find it interesting that people are using population as the reason Europe would win this hypothetical war.
By that standard, China would defeat a combined Europe and North America in a war. And a united Africa would be quite a force to be reckoned with. Which is a very funny thought.

Nobody would win since nuclear weapons would kill everyone!!

Depends on lots of things. Most importantly who is attacking who?

If it is ANYONE else attacking the United States then i is a win for North America. If it is North America attacking the continental Europe then it would be a much closer battle. The United states spends FAR MORE on military prowess than any other nation behind by a HUGE margin. The united states wins a battle on its home soil because of one simple factor. PROJECTION. No other country on earth has the transports necessary to bring their personall across the oceans to attack the US. Especially without the Worlds mos powerful navy knowing about it. America also has by far the most powerful air force which would be able to destroy all incoming aircraft and missiles.

Hence a defensive battle is a win for North America. No contest. As for attacking the US does have sufficient ability to deploy troops anywhere in the World and enjoys a technical advantage over any other military in the world. Given these facts I think THe US would eventually lose if they were to invade European Soil but they would get hell of a lot farther than Europe would get on the US