Compilations are usually put together on the cheap (the whole point being to resell something you've already sold), so I'd be surprised if there were too many remasters on them. I doubt the K-Tels of this world even have anybody on staff qualified to do that.
The quality of the compilation, then, depends on the "masters" they used. And I use the term advisedly, because there's no guarantee they didn't just tape if off a 45.
That said, reissue labels like Rhino often take care to find good-quality masters, so it really all depends, and you can only tell by listening.