Hi folks, I have three guitars with Bigsby's, and five Strats with factory trems. I love those Bigsby's and even wear a Bigsby T-shirt...
The initial question from rockin gecko was if a Floyd-Rose would fit in a Strat. My answer is NO. But... of course if you route the Strat tremolo cavity you might be able to do just that. KAHLER makes a vibrato very similar to the Floyd-Rose, that does fit a Strat without routing. It's about $170 at http://www.wammiworld.com
Both the Bigsby and the original Fender tremolos easily throw a guitar out of tune, that's why I'm only using them sparingly. But don't they just look great on a guitar? The Bigsby really dresses up an otherwise simple guitar and also provides a nice touch to your playing. Just don't bend that thing alll the way down, for gods sake... If you have to, then you really need a Floyd-Rose or a Kahler. Keep in mind that these usually require a locking nut as well, so the string can't "go anywhere" -out of tune for example.
Play on!