I did my undergrad's honors program and am now in medical school. (Bear in mind that what follows is specific to the particular program I was in at my particular school. It may or may not be the case at your school). I got As in all of the honors classes I took except for one, I think, so the "tougher grading" wasn't an issue for me. Although my participation in the honors college wasn't brought up in any of my interviews and probably wouldn't have made a difference whether I got admitted, it was TOTALLY worth it. I loved my honors classes. Generally speaking, the class sizes tend to be smaller, the professors tend to be more excited to be there teaching, and best of all the students were excited to be there learning. It was more challenging in the best possible way. The classes tended to be more focused on essays, class discussions, understanding and applying the material, ethics of what we were learning, etc. My professors and classmates really challenged me and exposed me to different perspectives. The program also included a capstone project, which for me resulted in a self-driven science research project that will eventually result in a publication with me as the first or second author (the grad student I partnered with is still working on his part of the data). Most of my best friends were also in the honors college.
So overall, even if the honors college didn't directly help get me into medical school, it was still an extremely valuable learning experience.