If you consider his age, you might aswell compare him to the guy in your avatar? Same age.
Bendtner punched them in for Birmingham in the start of the season, and in my opinion he would propably be best suited playing for a small PL club or a Championship.
He is arrogant, he is selfish, he hardly sees his teammates. And he isn't aware that he isn't the second coming. I doubt he will play a role in Arsenal with him not being as good as he thinks and his primadonna complexes. But as I said, I might be terribly mistaking.
I just think, Bendtner "came out" early, and we have seen the best of him. Don't expect much development.