It's not that simple. Assuming the $13k is the only difference between the two schools then that's virtually a rounding error in terms of monthly repayment. It's even more insignificant if OP will qualify for PSLF (I'm in med so idk how common PSLF-qualifying jobs are in PT)
For example, my school over-budgets for everything, and if one already has a reliable/paid off car with cheap insurance, they can "pocket" that money and live like a king. On the other hand, I know several schools (with tuition of 35-70k/yr) that squeeze every budget item that there's barely enough. Students at the latter schools will not have any extra spending money for misc expenses or emergencies
Anyways, $13k (even with interest) is a drop in the bucket if OP will be happier, more successful and less stressed at their preferred program. Every school will always budget enough to cover their tuition whether it's $30k or $90k/yr and some schools like to give more $ towards COL than others (regardless of what their tuition is). At my med school, everything from food, transportation, books, misc etc is overbudgeted (nobody buys books here), and I spend 70% of the food budget and 25% of the transportation budget, pocketing the difference in case of an emergency