Having kept both at one time or another, I'd have to say that their care is very different. Florida Softshells may be an exception. Here's my main reason...snapping turtles can survive nearly anything. You can basically keep them in sewage and feed them roadkill and they'll survive(I'm exaggerating, but you get the point). Softshells are not nearly as hardy in my opinion.

They do have some things in common; extremely heavy filtration, large enclosures, and bolted down cage furniture.