As a soldier in this modern fighting force I give this opinion.
The fighting man of WWII was a determined, tough-as-nails, gritty opponent on the battlefield, especially after surviving the first few months of combat.
The fighting man of today is also very dtermined, but not quite as tough(societal influence) or gritty. However, if you leave out the considerations of fire support and AFVs as the original question indicates you will still find a very well equipped, superbly trained lethal combat operative. The new tactics alone, in this soldier's opinion, give the modern soldier an edge however small. Add to this the incredible advantage of modern technology and I feel that the modern foot soldier would prevail.
You all havemade good arguements about weapons. Let's consider other equipment such as hand grenades, micro-communication, night vision, global positioning and body armor.
Taking absolutely nothing from the soldier who soundly defeated the Nazi menace is such a hard fought war, I still fel the modern soldier would have the undeniable advantage.