At my school you need to have a 3.5+ to be accepted into the Honors Program and you need to be in the program in order to take the honors courses. From my experience, Honors Gen Chem was MUCH harder than non-honors. My friend barely scraped a C in Honors Gen Chem, but passed non-honors Gen Chem with an A.
My rule of thumb with honors course is, if you are not interested in the subject, don't take honors. Honors teachers go more in depth into the topics than are necessary. They also expect you to go above and beyond with the material. It's not enough to just know the material, you also need to be able to use that and apply it to new situations (kind of like the MCAT?). I've found that in non-honors classes, I can get by with straight memorization, while with honors classes, I've had to learn the material inside and out.
I have found, though, that Honors English classes are A TON more fun than the non-honors ones. The classes are capped at 15-20 (I actually had a lower level honors english class with only 7 students, including myself) and are discussion based. We had no written homework and no quizzes or tests bar the midterm. Instead of a final, we just needed to do a creative project that connected the material we covered post-midterm.
Personally, I love my honors program and try to take as many classes in honors as possible (with the exception of Orgo). But it's up to you; would you rather get that 4.0, or would you be okay with a 3.4 though with a better grasp on the material?