Hi, I'm going to assume you're recording digitally. If not, ignore the A/D part of this. The tradeoff is this: if you compress on the way in, you have control of the signal level hitting the A/D converter, and can get a nice hot signal with good bit usage, without risking overs. However, you are commiting to the compression you record, and can't change your mind during the mix (you can add more, but you can't remove any).
If, on the other hand, you record, then compress, you have to send the signal back out throught the D/A, process it, then send it back through the A/D again. So, depending on the quality of the converters, your signal may suffer from all these conversions.
Myself, I like to use as little compression as possible when tracking, leaving my options open during mixdown. If you send a track back out to be compressed, it's a good idea to record the compressed signal to a new track, or at least make a safety of the dry track. I'm always changing my mind about compression settings as the mix evolves. For this reason, I like to use outboard compressors/limiters lightly during tracking, and then use software compressors during mixing.
Cheers, RD