Which touristy stuff?

Hilton and Towers is closer to more museums. It's maybe more "businesslike" and uniform. If you rent (or have seen) the Harrison Ford movie "The Fugitive"
then you will be familiar with some of the Hilton and Towers, where the final scenes take place.

Palmer House is closer to shopping/theaters/business district; it's more old-fashioned (fancy high-ceilinged lobby, etc.).

But they are only a few blocks apart; it really doesn't matter much.

My parents always stay at the Palmer House, for what it's worth.