You actually think this is a debate? Well lets put some key factors here:
1: America vs Europe is vague, how do you define Europe? Is Russia in the equation? Is Kazakhstan, Uzbekistan and the various other eastern European/Asian countries, does Turkey count?
Lets just say Europe is the EU plus most countries within those boundaries, I.E. Removing Russia and its more eastern neighbors out of the equation.
So running of that you have the United Stats Versus the EU who's main players would be Italy, France, Germany and England. The other countries would probably be taking orders from these powerhouses, or at least their contributions would be so little in comparison its not really much of a bother to put them in, lets put them in the group called the EU jr.
Again lets be fair and remove Nuclear weapons from the equation, obviously those put a slight damper on the war seeing as it would last about a day before the literal apocalypse. Also we remove the US troops from Germany as well they'd probably be eradicated.
So now we have the EU and most of the neighboring countries versus the United States, Nuclear weapons excluded and the smaller EU states lumped into a single factor. EU Jr, so there we have it. The tables set and were ready for war.
The United States Military has the highest budget, arguably the highest technological advancements, and oh Europe's newest best fighter, which is being designed here. The United States also has a large civilian force consisting of police, national guard and local militia that literally means we can empty our soldiers out of the country and maintain control while having the defenses to defend our nation from invasion, most European countries cannot boast this. United States also has the highest missile capabilities, more and more accurate missiles then anyone on earth. In air power the United States is also once more on top, from Stealth Fighters and Bombers to their newest fighter the Raptor the United States greatest weakness would be in the quality of their land forces in comparison to Europes, as well as the Tank technology, which many European nations have quite a good tap on.
The United States would be literally able to missile every square inch of any LZ needed in Britain to begin the invasion of Europe. As I said systematic bombings by fighters unable to be seen by even the most advanced RADAR upon British cities would be catastrophic, and then unlike the Germans the US would go ahead and bomb your country side which its planes do have enough fuel to enter. With its food gone and its population demoralized the UK would not be a good time to invade, instead sit back and let relief efforts start. Every time its halfway through the US would just do it again, crushing the UK's possibility on local food, starvation will be rampant.
After a few months of this the US would do another major bombing run, Napalm and missile attacks on every major British city and farm land. The US navy would then send in our carrier groups to do battle with the English navy, once more using our superior stealth technology upon your smaller fleet to slowly destroy it. British counter attacks would be minimal, the likely hood of them surviving all the way to the US is minimal, they could destroy a few cities but never be able to reap the damage we could from bases in Iceland.
Stage one complete.
Will write more later but am bored.
As for your invasion theories there Semper. you forget while there may have been no attacks upon ENGLANDS soil the British have always had an empire, which means every war fought in Afghanistan, India, various parts of Asia count in invasions of British soil. So yes..
There were of course other attacks while not invasions, a little humiliating.