I also face the same problem between Columbia University and University of Michigan-Ann Arbor.
Columbia university has very good professors but less active (in algorithm).
While Umich has smaller group with young professors and more active.
If I go Columbia, it seems that I will change to other areas such as computational learning theory or crypto.
I also have no ideas which one is more prestigious and how does prestige affect.
If anyone could give suggestions, I would be very appreiciate.
But if I were you I would choose UT Austin, which is one of my dream school.
It seems that UT Austin they do theory in more 'computer scientist' way.