Here's my opinion of Caltech(from a current student),
Caltech is first and foremost a research institute. They also happen to give degrees for research. The school is small and extremely prestigious. The program is small and interdisciplinary, you can work in any laboratory you want. There may not be many PIs, but the majority of the PIs at caltech are of the highest caliber. Social life at Caltech is so-so. Everyone is a scientist, and with that comes the awkwardness, gender-imbalances, and pockets of awesome people. The grad students at caltech tend to be pretty cool, the undergraduates horribly geeky. Counter-balancing this is the fact that LA is a quick trip away.
Stanford is a big university full of lots of people in northern cal. It's a bit deeper in the burbs than caltech.
Barring a preference for the PIs are either school, the decision would really come down to location and school size/dynamics.
Either choice is an excellent one.
Oh, the stipend system at caltech: You must be payed the minimum stipend. Whether this comes only from your professor or a combination of TA and your proffesor is a different manner. People generally TA for two years, and professors pick up your tab afterwards. If you want to TA more, it's 4.5k a class extra.