the current issue on the US spying on their allies in europe, my own country (Denmark) included, combined with the iranian fleet movement towards the us coastline as a result of US millitary presence in their country and several other places (south korea and other parts of asia are the ones that come to mind) has made me think about how tensions seem to rise in terms of what other countries are willing to put up with.

therefore i have been thinking about a scenario where Europe and north america somehow turned on each other in an all out war.

please note:

europe is not the european Union, but rather the official continent. this means Russia Joins the europeans.

North america has Canda and Mexico included in their forces

no nuclear warfare is allowed since no one would really be declared a winner after the fallout. ony conventional warfare is allowed.

neither side can surrender, but potential civilian guerilla warfare is not a factor. only real millitary might may be considered in this conflict.

so with that i would ask you whom do you think would emerge victorious? how long do you think such a battle would last?

As you are including Russia, EU would probably won. Both have considerable military forces, but the sum of all Europe militar forces would result in more soldiers. Then you got the biggest advantage of all, territory. The sum of the European continent with the asian part of Russia is massive and way bigger than NA. In a war like that you have to invade soon or later, and that extension is just unmanageable. Despite that, the cultural factor improves EU bets. Russians are a tough people, they survived and fought to death in 2 massive invasions. If NA passed the entire Europe and got in Russia, they would be debilitated and wouldn't be able to resist a harsh fight there. 

In a war, the two most important factors is how big your country is and how many natural resources you have to keep fighting. Technology helps, but if you don't have oil and steel it is completely useless. And in this aspect EU would have a advantage. That's the single reason why Germany lost WWII. They were massively superior technologically, the problem is that it was they against the world, or the limited natural resources in german territory vs. all natural resources of the world. Their only chance would be win the war so fast that they wouldn't run out of resources, but the sheer size of the territories they would have to conquer was a big problem. And back to your question, the NA or EU technology is nowhere near the massive advantage Germany had. Those guys had vastly superior machines than the rest of the world.

And, back to reality, a war like that wouldn't have a winner. Just look at how expensive Vietnam was or Iraq was. Both would end completely economically broken and the occupation of the loser would cost a fortune. USA, Germany, France, UK would be nowhere near the top of the largest economies ranking and the BRIC (except Russia of course, since they would be in the conflict) countries would enjoy a lot their reign as biggest economies "helping" the broken NA and EU to recover (and profiting a lot in the process).

Have a feeling internal strife would ruin Europe's chances against a more unified North America

Yup, pretty much this. 

isnt it human nature to set aside their differences when a threat approaches?

America would win because of superior quantity and quality of weapons, and the ability to act with one purpose.

valid points indeed.. although the US wouldnt necessarily have to invade at first, but instead maybe use their focus on a naval siege of the UK to cripple them and really hit them on the western coastline where some of the richest countries i.e france, scandinavia etc. is located.. it would be a long battle of starvation but it is the best way of winning i see for NA..

that being isaid i personally agree that europe would propably be the "winner". although as you mentioned. China might be seeing an oppurtunity and sweep in.. a new world order would be established no matter the outcome between the two.

America has weak and naive leaders, it would not be hard for even New Zealand to win.

It would be close, but if those Canadian snipers live up to their name and legend, it might edge NA ahead. Now if China somehow slipped into the European mix :P

Now why would China ever do a thing like that? lol