What is better for your feet -- wearing flip flops or going barefoot?

Neither: Wear good shoes is the primary answer of course.

There is a whole: Debate about barefoot walking/running. Personally, i think we were born barefoot and there is nothing wrong with barefoot walking unless it hurts. Running is a different issue because nowadays streets have hard pavements and the hard pavement is not flexible like a dirt or grass floor and stress on asphalt may cause injury. Nowadays, flip flops with arch supports are available as well.