Survival Horror is basically action horror with the difficulty drastically turned up and a few "play it smart" options added. Fundamentally, in A-H there is no choice but to fight, and is balanced around that. S-H is mechanically very similar, but the enemies are stronger, item drops are rarer, and the player is encouraged to find alternatives to fighting.
Basically, in A-H the player is directed into fighting the monster by the designer. S-H adds that the player is never allowed to properly prepare for a fight, and there are usually some alternatives around.
Other than that, they're basically the same thing.
If I had to pick, though, I would say S-H is better because it includes all the A-H design choices and then adds its own. You can always turn a S-H game into an A-H game by turning the difficulty down and playing like Rambo, but the reverse is not true.
