As I understand it :
Slow action = rod bend is over the greater portion (length) of the rod. Or in other words, a "soft" action, or parabolic bend. The rod bends in a shape like this ... )
Fast action = rod tip bends easily, but majority of rod length is stiffer & offers more power (on hookset & fish fighting capabilities). Rod bend is more of a "J" shape
Don't know as there's much advantage/disadvantage to either ... they both work - I use rods that have both "actions", and use them interchangably (for the type of fishing I do most ... as in "casting/shooting jigs"). They "are" different .. but, if you have your drag set correctly, for the action (power) of the rod, then you don't usually need to think too much about it :p
I set the hook the same way, regardless of what length or action rod I'm using ... because I know I've set the drag to give, before the lb test force has been exceeded.
... cp