Funny this question comes up now--I noticed something today that directly speaks to the answer.
I was watching PTI today, and during one of those interludes they intersperse among the commercials, they showed a high, wide-angle POV shot of the set. In the top corner of the screen, you could see what looked very much like part of the ATH set. Based on that, I'm guessing that both shows are filmed in the same studio--the PTI set on one side of the space, the ATH set on the other half, with the cameras located right in the middle. They record ATH, then swing the cameras around 180º to shoot PTI. Hence, Tony Reali doesn't need to go far to switch from one show to the other--he just moves to the other side of the room.
I don't know if they're live or not, though they do seem to be on top of fairly late-breaking stories most of the time. I'm guessing Justin is right, that Five Good Minutes is taped, and the rest of it is live. The "toss" to SportsCenter at the end of PTI seems to happen in real time, though perhaps they're just smooth with it.