I use the two for slightly different things....
The Mustang Trem is my replacement for a Floyd Rose in my arsenal. I like the feel better, I like that it's slightly less responsive, and because the bridge moves, I have a few Steinberger Trans Trem type things I can do with it (like I can bend the pitch of the Low E down 3 whole steps and hold a power chord in tune enough to use it in a song), plus if I'm covering Van-Halen I don't need to switch to a guitar with a Gibson style bridge setup to play "Running with the Devil", because I already have the strings behind the bridge, AND the Whammy Bar. The Mustang trem is like having your cake and being able to eat it too. I don't need bloody hex keys to unlock the nut to tune, and if the string path is that stable to keep it in tune, I don't need any of that hex key crap anyway. I even found modifying one to take a foreign thread Strat bar means you can use the excess coming out the other side as a trem lock when restringing. Last time It took me about seven minutes to restring.
However, the Mustang Trem does go out of tune if you drop tune (because it floats and is more responsive), that's where my Jaguar and Jazzmaster guitars come in. I notice that the tuning changes very little or not at all when I'm using drop tunings on those, and when running a Jaguar or Jazzmaster at double drop C (C,G,D,G,B,E), dive bombs like a vintage Strat trem are very possible - on my Jaguar the strings almost go as limp as they do on a Floyd Rose. I've never had one that went out of tune - on ANY Jaguar or Jazzmaster I've ever played - with a TOM or a Stock bridge. I get around the "moving string" issues on the low E by shortening the screw and adding tighter springs on the high and low E String saddles to make things more stable. I also aid this by keeping my palm near/on the bridge most of the time, holding the strings down.