That is a hard call. With the difference in mileage - that is almost a wash. 100K+ miles is really nothing on modern fuel injected cars, assuming that they were well taken care of. As for dependability - unfortunately, we don't have a crystal ball to look into. Even harder to choose, as each one (generation) has its known issues. Could even go further and say that compared to other models, model years, even other makes - every single vehicle you find out there will have some sort of "issue". The trick is finding which car has potential issues you can live with / address.

The 2001 Corolla:

The 8th gen model has some of its fair share of oil consumption issues. Just do a quick search of 8th gen Corolla (model years 1998-2002) and you'll see all sorts of posts on people having problems with excessive oil consumption.

Note that not all 8th gen Corollas have this issue, mine has been pretty much flawless on that respect (2002 w/205K original miles) - but I've had the other common "fun" problem of the hard to get rid of EVAP related codes.

The 2006 Corolla

Being a 9th gen model, has addressed many of the issues with oil consumption and EVAP codes from the previous generation (mostly mechanical defects in nature), but also added some additional issues with the DBW throttle system and revised electrical system. Some people like the throttle, some don't. I personally felt them to be either very lazy in response to conventional cabled throttles or overly sensitive - depending on the calibration state.

The second half of this generation was also involved with the media frenzy involving SUA (sudden unintended acceleration) - as well as not as well covered sudden unintentional stalling / shutdown. Root cause is still unknown - some cars have experienced these behaviors, some have not. Some required replacement ECMs - some went all out and replaced ECMs or reflashed existing ones, replaced electronic throttle pedal assembly, clipped pedals, etc. Same as the 8th gen, just do a quick search online and find out what other owners are saying.

Bottom line:

If you can get an extended test drive, if at all possible, that might be the deciding factor. Both I would considered very reliable, all considered - but like anything, you can get a unit that has its quirks / become a maintenance nightmare (ie, lemon). I'd just see which one "feels" most comfortable to you and your daughter, driving-wise. You can have the most reliable vehicle out there, but if it is not comfortable to drive - pretty much useless IMO.