I've found it worth it, and am listing it on my application (although I don't expect it to matter much, with one exception).
1. My honors classes tend to be better experiences than my non-honors classes. Small class sizes, engaging discussion, great professors, and intriguing work. My upper level major classes are small and I enjoy those too, but honors classes are on another level.
2. I've gotten to know the Honors College staff very well, and they've been money in assisting several student organizations I'm in. Helping set up a 501(c)(3) account, finding graduate students for social work / education purposes, setting up a class, etc. They have connections, and when they know you personally, they can help you reach your goals.
3. As a honors student we're eligible to receive grants for research, travel, etc. Every student receives a scholarship upon enrollment. The Honors College seems to be the only department of my university not having budget cutbacks.
4. You get to register early, you get the best housing on campus, the super cheap Maymester abroad courses are available only to you, etc.
5. They require a senior thesis, but that sort of intellectual project is a good thing in my opinion. Many medical schools like research, so if you can match that up with your thesis, you're golden.
6. One of my state medical schools adds boosts to students' GPA depending on the school they come from. If you come from my university, you get an extra 0.25 (I think that's the value) added if you're in honors than if you aren't.
So many reasons I like the Honors College, no drawback (although for some friends, the thesis isn't worth it to them). Even if it didn't help me at this one school, I;ve enjoyed it.