No, the grants are just based on your GPA SAT/ACT stuff. Nothing having to do with the honors program. The state school honors program is just more "well known"
Ok. Well, then here's my full suggestion.
Go back to your old school if that's what would really make you happy. Honors programs will not add anything significant to your degree, so if you love being in this particular honors program, stay! If you don't, get out so that you can take whatever classes you want and not worry about the special requirements for the honors program.
Schools use honors programs to attract bright students, but unless those honors programs confer some sort of financial benefit OR the students find them more rewarding OR they confer some other kind of tangible benefit I'm not aware of, they don't add anything particularly interesting to your degree. Medical schools, on the whole, care more about your GPA than anything else (tied with your MCAT score, of course), regardless of what program you're in.
In addition, regardless of your honors program status, you can list this scholarship that you received on your application. It will let any admissions committee know that while you probably could have attended another college, the one you were at thought you would be a great enough student that it threw money at you to get you to stay. That means something, and admissions committees know that, even if it doesn't impact every admissions decision they make.