The most important difference between 1944 and today would be in the realm of guided munitions. I once heard that a single F-15 packs as much firepower as an entire squadron of WWII era bombers, when you take into account explosive weight and the percentage of ordnance you can get on target (Keep in mind, the F-15 is a Fighter/Bomber, not a dedicated bomber. If we start talking about the B-52, things get even crazier). Additionally, Naval Gun Fire support has come a long way since the 1940’s. US destroyers and cruisers now only come equipped with one or two 5″ main guns. In the 1940’s, 5″ guns were almost considered an afterthought. With improved fuses and nearly automatic rates of fire that can be achieved with today’s weapons, you wouldn’t need the hours and hours of shelling they used during WW2 landings.
As far as the landings go, with today’s amphibious landing tactics and equipment, you wouldn’t NEED to land at Omaha beach at all.