As explained by Ser Barristain, Rhaegar was never a real warrior. He never had to fight for his life in a real battle.
Robert was an immensely strong warrior who fought with a very heavy battle axe forged specially for him. Rhaegar never stood a chance.
(That being said, the most skilled swordsman, Ser Arthur Dayne was killed by the crannogman Howland Reed (Jojen & Meera's father). He was a small man and crannogmen don't use longswords or armours.)
The sad thing about Robert is that he can never leave a legacy. He has no trueborn sons (only one was aborted). And when the battle of the dawn is won (assuming it will be so), Rhaegar will probably be remembered forever as a great hero (humankind stands a chance only because of the plans he made).
So, Rhaegar never really lost. He won. Robert never realized that.