ok, my rundown on this... If i'm wrong (which I most probably am, just tell me i'm a dopey f*ck and be done with it!
Flexier: more release off the top and give the board a more alive feel
Stiffer: make a board feel a little more "grounded" which in bigger surf can make the board feel more solid under your feet instead of skiddish
Twin fins: on the right board they can make it ultra fast and loose, but tend to be harder to work on your backhand
Quad fins: again it varies based on the board you've got them on, but can offer you unreal speed down the line on long walling waves but can be a bit slow/hard to get a turn out of them at certain times