In my experience there are 2 main differences in favour of the sinking lure, and 2 in favour of the floating. So each becomes more useful on it's day.
Sinking advantages:
The stop and start retrieve, or twitch and pause, gets the best from a sinking lure. Stopping the lure obviously does 2 things. 1) allows it to drop down and/or back towards any following fish (look at how many fish have been caught on the drop this year...), and 2) allows it to maintain a lower position in rougher water - if you stopped a floating lure in such conditions then it'd obviously float up and get battered in the wash. A sinking lure will stay submurged so be a more effective fishing tool. Those are the 2 main advantages if you ask me.
Floating advantages:
In contrast, there will be days when fish are either above the lure (like Keith's recent description of bass swimming up and turning back down on schools of bait), or when they actually just prefer a presentation that leaves the lure drifting away from them, upwards. That's on the pauses at least, if you use any. No pauses = practically no difference between the two - unless their weight's are different, in which case the lighter (floater) is likely to have the wider action. So the 2 advantages of a floating bait over it's brother, sinker, is again a different presentation, but also a subtley better action.
Hopefully that makes at least a little bit of sense. There are more finer points too I'd imagine but to sum it up:
Floater: Calmer conditions (when you feel you don't want a sinking presentation), slightly better action normally, easier to get out of snags (I actually like to give it a bit of slack and shake the rod tip from side to side without putting any real pressure on it. If it's on rock, quite often it will gently wiggle itself loose and float upwards and away).
Sinking: Rougher water, longer casting, drops back towards a following fish rather than floating upwards and away from it. More difficult to get out of snags, unless you just puuuuuullllll.
Each has their day. Definitely!