The Mustang bridge corrects two things most people don't like about the Jag/JM bridge which is strings jumping out of the grooves when played hard, and a mechanical buzz inherent with those bridges (there is also a product called a buzz stop, which I've never explored. I don't have a Mastery bridge (yet), but from what I understand, it alleviates all those problems, plus is easier to intonate, and transfers more string energy to the body of the guitar, increasing tone and sustain. It also makes the string spacing a little tighter, so the E strings don't roll off the fretboard. It's pretty universally loved by offset guitar players. There's another product on the market now, called a Staytrem bridge. This is supposed to do most of the stuff the Mastery does, but looks a little more traditional, and might match the aesthetic of a vintage guitar a little better. It's also cheaper, so easier to swallow when upgrading a Japanese Fender or Squier.
Mustang guitars are a whole other animal. I have only really liked the vintage USA ones (I know, what a snob). They come in a few different flavors - both 22.5 and 24" scales and A (narrow) or B (wider) width necks. My favorite is 24" scale with a B neck, but there's something to be said for the A neck, especially if you have small hands. A widths are pretty fun to solo on, because all the notes are close together. If you find a good one, they sound great and are a lot of fun to play. They're nice and light too, which is a bonus to me these days. The trems are a little wonky and not much good but for the occasional little bend. Unlike the Jag, the switching is reasonably simple. A switch for each pickup. In the same direction, they're in phase, opposite directions, they're out. Also, unlike the Jag, all options are very usable tones. The drag here is that nice examples usually go for between $1200-1500 depending on color and condition. For what was essentially a student model guitar. Thanks Kurt Cobain.