It just depends on the model, and the project, or gig. I say "model," because just saying "POD" or "Tonelab" or whatever, just doesn't get specific enough. I've found one amp model so far that Line 6 has that really is great... it's their plexi model. I've used it on a ton of recordings, mostly those I've been hired for, but it still sounds great to me. One world-class guitarist that uses a POD for his live shows is Lincoln Brewster. I had the pleasure of an extremely unique learning experience with him. It was during a large music festival a few years back. In the morning, I was able to attend a small seminar he gave. He answered questions, many about his tone, and touted the POD as his tone source, saying that he needs the consistancy it provides when he travels and doesn't take his own PA, like at the large outdoor music festivals. In the afternoon, he played in a large circus tent for about two thousand folks.... he even stopped the show to ask the FOH engineer to solo his guitar, so the folks that had been at the seminar could hear the POD. That evening, he was on the main stage with about 40,000 people outdoors at the amphitheater. In the smaller concert, you could tell he was using a pod, but it still was very passable. In the large concert, you could not tell, and it sounded great.
That said, one of the best tones I've heard a guy have live is Eric Johnson. To explain his rig in this post would be too much, and make a long winded post more like a book. BUT, if you study his rig
HERE <-CLICKY, you'll see that he goes to great lengths to process his live sound just like in the studio, adding time based effects after the microphone and controlling the whole thing from the stage. When you think about it, this is what a modeller is doing...the whole processed studio-like sound. This is the approach I've taken live, but you have to have a great monitor system. I use a hybrid approach... running a modeller into a 30 watt class a poweramp, and then into a speaker which lives in an isolation box (so I can crank that sucker without hearing the sound man cry.) This is the best really.... the flexibility of a modeled preamp, ran into a cranked to the max 30w EL84 tube poweramp, into a 12" speaker miced with an SM57, then into the board where my reverb is added. Then I have my own monitor mixer by my side, and a sweet pair of in-ears. The sub is just under the stage beneath my feet, and it tickles my feet when we play. It works well!
Peace!!
~Shawn