More criteria please! There will be lots of answers anyway, but what do you want out of the amp? Requirements? Budget? Musical types/directions? And are you thinking LS Classic or Special? Or is that part of what you're figuring out?
I assume you're into a good clean sound, because these two (three, actually) amps theoretically represent the peak(s) of Mesa's clean tones. They tend to appeal to the blues/country/jazz and lower-gain players around here. I'd assume you know this, as well as the basic features of each; so you probably know the Angel doesn't do channel switching or have a Gain + Master volume config. They're heavy and built like tanks.
The Blue Angel is supposedly like a Fender Deluxe with some cool power stage options. If you just want a sweet, medium powered amp with few/no frills, just a great old-school Class-A clean tone, the Angel is a good catch, especially for the money, usually. I haven't played one, but I want to and every time I see one listed I look at what I have to sell. But I don't really need it because...
The LSC is the full-on fashizzle, for what I do (funk, R&B, low/medium-gain rock). Powerful, versatile, configurable, and addictive. The clean channel is simply amazing, and you can dirty it up without too much complaint from the neighbors. I have not yet heard the claim as to which has the superior clean tone, and I can't say myself... but the LSC's is pretty damned sweet. The drive channel usually needs a bit more volume to get going, and it's a controversial entity around here (lots of mods/debate/tricks to play with and argue about). Also, the Classic has a few more options than the Special, fwiw. Tweed AC setting, power tube options, and some other stuff. The Special's a nice little amp, though I think I've heard more reliability issues about the LSS.
If you need a fair amount of clean headroom, the LSC is probably the thing. Otherwise, it all depends on your remaining requirements. I wish I had one of each.
But I'm happy as a pig in merde with my LSC.