There isn’t a real difference in prestige here between the two schools. An extra 160k with compounding interest is a lot of money. Unless you feel like you’d be absolutely miserable there, pick LSU.
I agree that the prestige difference probably isn't that big, but the schools probably do have varying regional reputations. LKSOM has far more connections in the Northeast while LSU with the southeast. If OP wants to do her residency in the Northeast, I'd say she'd have a much easier time securing one at Temple. If she doesn't care which region she does her residency, then I'd go with LSU.
In terms of paying 250K+ debt, here's some of the more popular (and smarter options)
1. Public Service Loan Forgiveness..... Betting your marbles on this program is risky due to the on and off talks about it being defunded or changed so that it will no longer be of use to medical school graduates. However, if the program is unchanged by the time you graduate, it's a viable option. Pretty much, you have to do your residency/fellowship at a non-profit, qualifying hospital (most academic hospitals will qualify), and then also work for a qualifying hospital/institution after your residency/fellowship until you reach a total of 120 months of payment. The program is best when you sign up for income-based repayment (PAYE/REPAYE). If everything works out, this plan could save you hundreds of thousands of dollars.
Here's some more information about it that shows you the potential huge benefits. I think I read a statistic where about 40% of graduating medical students choose this route of repaying back their loans.
Deciding to go for Public Service Loan Forgiveness is a big decision. We ran the numbers to help attending physicians decide if PSLF is your best option.
www.whitecoatinvestor.com
2. Refinancing your loans after graduation.... Refinancing your loans at a lower interest rate will lead to less interest increase, and more manageable interest increments during your time in residency. I highly advise not to defer loan payments during your residency as it will just lead to more money you have to pay back. This is probably the best route if you don't want to work for a non-profit institution after completing your residency training due to a potentially higher salary increase you could receive.
3. Negotiating contract with your employer... often times employers may help you pay off your student loans, especially if you're serving a rural or underserved area.
Overall, you want to be smart and seek guidance when paying your loans. Talk to your school's financial office and also look at resources such as the White Coat Investor.