Is it worth being a decent student in a well accredited university or a great student at a normally accredited university?

You should apply! There is a difference in the quality of education you receive from one school to the next. If you feel like you're not being challenged enough and want to go to a better school, I would encourage you to apply. The name of your school does make a difference on your resume when you're being compared to other candidates while applying for a job.

I think it depends on your personality and ability. I personally consider myself a bit laid back. I can work hard and be dedicated as well as handle pressure, but I don't like being constantly in that environment. I personally like the environment of diverse backgrounds (ethnic, religious, wealth, ideology), which is more likely to be found at a public university than a private university. I also like to be appreciated for my effort and results, which as an above average student is quite often recognized.
One advantage of a public institution is, that as a very good student at a good public university, I had more opportunities for scholarships and grants. I could still get access to quality faculty and resources if I looked for them and thus still get a Ivy league school-level education by working hard and being disciplined to learn and succeed. However, a big advantage of Ivy league schools is, if you don't a financial limit like many average students do, the prestige and access to great minds and resources that can sometimes be unparalleled to public institutions. The resources and networking available can be as big as the problems and challenges addressed and solved there. So at the end of the day there are benefits at both institutions depending on what aspects of those benefits appeals to your personality and mentality.