Being a Java based program, and not one apparently heavily tested on the Mac, Azureus definitely has a lot of quriks (mostly in funky screen redraws), but it's still far and away the best BT client on the Mac. Some of it's advantages:

-Massively detailed control over everything (can be bewildering, but also useful)
-Great download/seeding management, including full statistics between launches, different handling of finished downloads left to seed, and automated file management
-Incredible detailed info on what's going on (exact parts being transferred, etc)
-Handles non-English filenames relatively smoothly (the standard Mac BT client is completely incapable of downloading some files with non-English characters in the filename)
-For a Java app, relatively speedy (generally under 5% processor use on my G5)
-Under heavy development (has gone from unusable to great in a couple of months)

I like the standard BT client for it's simplicity, but for any degree of control, or if you want to download anything with a non-English filename, Azureus is the only way to go.

By the way, it's generally quite stable, but has a habit of crashing on quit. This hasn't caused any problems, though.