fixed bridge is pretty much um fixed bridge, stays there and doesnt move.
pros:
-easy to restring/tune
-you can change tunings on the fly.
cons:
-of course, no divebombing like vai or whammy effects.
Floyd rose is a knife edge floating bridge. Exists in many different form, Original or licensed(inferior). Some ibanez tremolos are known to be of good quality though, even though its a licensed version.
pros:
-whammy of course, and divebombs and those tricks.
cons:
-a hassle when it comes to changing strings, especially when you're a beginner, get someone to teach you
-you cant change tunings on the fly, like you can with a fixed bridge, so when jamming, stick to one tuning.
-when not set up properly, may cause tuning problems.