Setting is in a hideout of the Red Skull's both are at peak fighting strength and have a full arsenal of weapons.
Although it ultimately ended up as a stalemate in the crossover, Red Skull exhibited superior fighting skills...
Plus, even below his physical peak, he's had some very impressive physical feats. Not sure how it might turn out with their full arsenal of weapons, though... Sure Red Skull would probably triumph Joker in that department too, but I'd imagine Joker would have some tricks up his sleeve to keep things interesting.
Joker is a slightly better character than Skull, but Skull wins 10/10.
Joker really has little to no fighting skills, Skull is a great fighter and (although I haven't seen him win) can hold his own against Cap in terms of skill.
Joker is a psychotic genius, and is good at setting up scenarios and playing tricks on people but in a straight up fight he's toast against most people.