Pretty much the same results except a slightly longer war and more casualties. There was no way of ensuring a Nazi victory at any point after Stalingrad but let us assume we are left without Hitler's incompetent leadership for the last two years of the war.
I could see whomever is Nazi leader, whether it's Goring or anyone else would not have invested capital into the sinkhole that was Italy. Good chance they put up a token defense and leave the cream of their remaining troops in the Eastern Front.
No way of really stopping the Russian juggernaut headed their way. But good chance they don't gamble the last of their remaining offensive capabilities in a foolish gamble at Kursk. More likely a slow protracted retreat back to the borders intent on inflicting as much pain on the Red Menace as possible.
In the West, if there is even moderately competent leadership, they would leave Italy behind and build a defensive firewall along the Alps. Rommel would be empowered to crush the Allied landing. While there's a good chance they would not be so easily fooled on the decoy landing at Calais, there might also not be any way of stopping the actual landing in Normandy.
Rommel could have spread his forces out more evenly in a way to react immediately to any landing. I imagine this version of D - Day would be a lot bloodier than IOTL and Nazi's might not be able to drive the Allies into the sea but be able to hold their own for a little while. Eventually allied naval and air power would be able to open up pockets of openings along the lines to allow Allied overwhelming manpower to drive through.
Overall I could see a Hitler death extend the war a whole Calander year but would that really be a good thing?