In my opinion, you should take out the federal loans and only federal loans.
1. The 6.8% rate is for the Stafford loan and you can borrow up to $20,500 a year on them, no questions asked, and Stern's tuition is certainly more than $20,500, and I don't know if they even give scholarships to part timers, but most programs don't at all, or at best give minimal scholarship funding. The private loan at 5.25% is variable and will likely go up once the feds raise rates since they've been really low for the last several years. Some guys here however have been able to find private loans at lower rates but had to do so with a credit-worthy co-signer. Some of course had good enough credit to get that great rate anyway.
2. You should be allowed to apply for a PLUS loan as well at 7.9% fixed APR. That loan you can use up to the cost of attendance, minus the 20,500 for the stafford at 6.8% and any other aid you have.
The biggest advantage of federal loans besides a fixed rate, even if they are higher than private counterparts are loan repayment options. With the federal loans, you are likely going to be eligible for IBR payments to keep your loan payments reasonable if for whatever reason you do not work in a position that earns you decent money, though yes, the interest will still accrue the same way. You will probably not have that with a private loan. Also if you work in the fed govt after 10 straight years, the feds will forgive all your loans that are federally backed. You won't get that with a private loan. If you don't work in a govt position, loan balance is forgiven (but I believe there is a tax waiting) after 20 years. Most people should be able to pay their loans off in 20 years even with IBR assuming they work diligently and continue to move up the ranks, find better fitting jobs, etc.