Without knowledge of the special provisions of your loan contract, the one with the highest interest rate should be paid first.
Or, if one's fixed payment is much larger than the other, and it is a burden, then it should be paid first, but refinancing may be an option.
Socially speaking and possibly even economically since it could affect your reputation, it is probably best to either refinance the cosigned loan or pay that off as rapidly as possible.
Economically speaking, I would recommend no prepayment since the asset that is leveraged is your mind which will last many decades, probably exceeding the term of the loan, but some caveats must be handled first:
- Fund all future outflows, risk-adjusted, with credit purchases, like deposits, commercial paper, short term treasuries, the last two in the form of ETFs or equivalent thus no direct exposure.
- Insure income for as long as the life of all loans that one owes.
- Buy as much hedged world equity as possible
Many would disagree, but I finance the way I play poker: tight-aggressive.