True about finding out the HPSP before NHSC, but I wouldn't tell anyone to base it off of disadvantaged status. I am one of the least disadvantaged people you could find (dad is a dentist, got full-ride scholarship to undergrad thus no undergrad debt, etc) and I still got the scholarship. Apply for both, especially since they aren't at the same time. If you get HPSP, then keep it. If not, try the NHSC.
...Although, that doesn't really answer the original question. You can apply for both, but only in the order I said above, which is lame, but the only way to do it unless you want NHSC over the HPSP, then maybe try NHSC and then HPSP for a 3 year? Although I hear those are rare nowadays.