I definitely recommend public. The best job I have ever had is my present job as an engineer with the DoD. Opportunity all over, pretty much automatic pay raises, lots of chances for promotions and travel including international, good people to work with, no cutthroat co-workers, easy to change locations and transfer, usually no penny pinching (not now though). Much more security with public. Private sector will lay you off in a heartbeat if the profit even looks like it might nosedive.
With public, you can do as much or as little as you want. Your choice.