This is of course little more than anecdotal evidence, but I don't personally know of a single person that enjoys Big Bang Theory. In contrast, I hear nothing but praise and excitement concerning Community.
For me, Big Bang Theory at best just feels hokey and formulaic. It doesn't even try to distinguish itself from any other sitcom. That is, of course, why it's popular though. It doesn't need to be different, apparently. Most people don't want different, whether it be television, film, music, food, whatever.
On the other hand, I watch Community and am consistently amused. It's generally witty, fast-paced, and often outright surreal. It has a formula as well, but it's aware of it and openly mocks it. It's the only sitcom I watch, actually. I generally just don't like the genre, so I think it speaks volumes in Community's favor that I look forward to each episode.
Watch what you want. It's just sad to see Community struggle when it has absolutely everything going in its favor.