Bigsby trems seem to work very well on many styles of guitars: solid, semi and full hollow, as long as one installs the correct version on the guitar (for flat solid-only surface mount, short tail archtop, long tail archtop ...) Besides, semis and hollows, I've seem Bigsby trems and their clones on LPs, SGs, Teles, Surf guitars (Jazzmaster-type), Reverends, Gretsches, Ibanez Artcores -- but never (or rarely) a Strat, Super-Strat (usually FR) or clone. The (Super-)Strat exception is likely because these guitars already are designed and built around their particular trem systems.
Bigsby trems are known for preserving or improving the general tone of the guitar, as opposed to some other trem designs that radically alter sustain and suffer other ill effects (lots o' trem gargle). A Bigsby is not a dive-bombing trem, but typically delivers the more subtle, shimmering trem found in the rhythm guitar of surf, rock-a-billie, some swing and some country. It will do rock and alt duty (John 5 and Joe Perry as noted), but ain't a shredders trem. Shred-land is where you will find Floyd Rose and Strat floating trem.
If you add a Bigsby to your guitar, you also may need to change the bridge -- a roller bridge is best, but a normal Tune-O-Matic will work if will 'tilt' back and forth with trem action.