My impressions would be (based purely on home use, I'm afraid):
Rebel Yell - bright, upper-midrangey, not a lot of bass. The most "modern" sounding of the three.
Crawler - very middy, quite dark, growly/snarly kind of tone.
Black Dog - lower-midrangey but with some bite. Maybe the most "vintage" of the three, but best at blues-rock to old school hard rock, rather than being a real all-rounder.
What about the Abraxas? I haven't tried it, but it seems that it's somewhere between the Mule and Crawler, a nice warm beefed-up PAF sound.