The question really isn't if a bigger, better trained, better equipped, more experienced and better led army will beat a smaller, less experienced and trained and poorly led army but what happens when a veteran, well led, well equipped army that is 2/3 or 1/2 the size of its opponent who are all raw recruits, poorly equipped and led or more accurately and realistically when each army has different levels of superiority/inferiority in these factors combined with terrain and the need to play either offense and defense. If you want to take Americans vs Germans look at the performance of the US 106th division in the Battle of the Bulge. This was a raw, inexperienced, new unit that was put in what was thought to be a "quiet" sector of the line to get some "seasoning". They were overrun (2/3 surrendered) by experienced German troops in the biggest defeat of the war (worse than Kasserine Pass). Compare that with the 101st Airborne in Bastone -- a veteran unit (but not equipped well in terms of anti tank weapons, armor to fight panzers) that was superbly led that stopped the Germans cold and even though surrounded held on until Patton got the rescue force to them which in turn totally derailed the German offensive.