Have the same problem with the tightie-whities...cut into the buttocks a bit. Last long trip, I tried the boxer brief style of drawers and made a big difference. Didn't go expensive as I wasn't sure this style would work but it helped out tremendously. I tried Hanes, Fruit of the Loom and Joe Boxer brand. I looked at the expensive long-distance brands but for the price difference, I couldn't justify not going with the regular brands (I'm sure others of our group will expand on the more expensive stuff). However, I thought of the three I tried, I liked the fit of the Fruit o' da Loom brand boxer brief...seemed to stay in place better than the Hanes or Joe Boxer.
Good luck on however proceed but my opinion, start cheap first to see if it works for you. I couldn't justify spending $10-$30 bucks for a pair of drawers and find out I didn't like 'em.