I went through this a few years back, and wound up with a Sterling.
Sterling:
Smaller body, slimmer neck with a more narrow nutwidth (strings are closer together). It's lighter, smaller and more managable. IMO, the Sterling can do any sound the Stingray can do, and more. The electronics give you more options. I find in the flat vs. flat voicings that the sterling is a little darker, but mine has a rosewood fingerboard...and sounds a bit darker than other Music Mans i've played, other sterlings included.
The pickup selector is a nice touch. You can make it sound like a 'ray, or appromimate Fender P and J bass tones as well. There's a lot of versatility in that pre-amp between the pickup selector and the 3 band EQ. I just love the flat tone of the bass. I'm a simple player, and just set everything flat and play. But it's nice to know the other tonal options are there if I ever need them...which does happen from time to time.
If you're used to playing a Sterling, every other bass you pick up feels like a clumsy slab of wood in your hands. If you're used to a bigger bass, the string spacing can feel cluttered and the body can feel small. The Sterling is so effortless to play, you have to fight with other basses to do the same thing. But, on the other hand...if you're used to a bass that requires a little more oomph to play, the Sterling may feel a little TOO managable. It's all personal preference and conditioning.
Stingray:
Bigger body, wider nutwidth (strings spaced farther apart). It's a bit heavier and just plain bigger in every way. In general, i've found the flat voicing to be brighter and more aggressive than the Sterling...but again, my Sterling a rosewood fingerboard. If you're used to a hefty bass like a P bass or something similar, the Sting Ray will probably feel most comfortable right away. The neck is like a P bass neck, but much more playable. Music Man basses practically play themselves, even the larger Sting Ray.
Anyways, the Stingray seems to be the more popular model. It's also cheaper. I liked the Sterling enough to pay the extra cash without thinking twice. 2 seperate studio engineers have told me that bass has the best sounding direct signal of any bass they've recorded. And i've gotten similar comments from sound guys at clubs a bunch of times. They're just fantastic instruments. I want another bass as a backup...I want another Sterling.
Hope that helps. Like others have said they're differrent, and it comes down to personal preference. Now that you know the differences, play both and let your hands and ears decide.
-Nick