The biggest issues I have with Big Bang Theory are to do with the representation of geek culture as something laughable: characters are portrayed as being so immersed in it that they are socially inept, awkward and almost constantly the butt of the joke. When they are not, it's Penny who receives verbal abuse due to her not having the same level of education as the others.
There's casual racism and homophobia in the portrayal of Raj, casual sexism towards most of the women, overt sexism and general creepiness in the behaviour of Howard (who is still a main character, and whom we are supposed to 'like' to an extent). Particularly upsetting was the episode in which Bernadette, Penny and Amy visit the comic book store - a potentially good set-up that only turns into the usual and outdated (if only) 'oh but women just don't get comics'.
This piece is a very good comparison of the two, that also does not thrash one over the other: http://observationdeck.io9.com/communit ... 1509523444
And this, while I disagree in the tone, is a good summary of why I prefer Community over Big Bang Theory:
Paintballing (twice). Glee. Dungeons & Dragons. Pulp Fiction. Community constantly pay homage to pop culture cleverly. There’s actual – *gasp*- writing involved. The Big Bang Theory uses references to things in pop culture as punch lines. Nothin’ but laziness there. (from http://www.gollancz.co.uk/2012/12/10-re ... ng-theory/
I suggest you watch the episode Advanced Dungeons & Dragons (Season 2, episode 14), in which the game is used as a way of looking at body issues and suicidal depression.
(Also, and not to be underestimated, is the glorious lack of laughter in Community. I cannot stand recorded laughter.)