"Applied physics means spending time in lab crunching numbers, estimating errors, writing reports, and such. Theoretical physics means spending that time instead with the theoretical side of things, and problem sets, and advanced math courses, and the like.
If it's a good university, either one will mean that you've worked your *** off on physics. And both will have lab time et cetera. It's just a question of what you'd rather focus on: would you rather work in a particle accelerator, or would you rather work in string theory and other more-theoretical more-pure-math work?"