I was as big of a homer for Trent Edwards as there was on this board, years back.
I am very familiar with Trent but at some point in his career he got to the point to where he often times would almost immediately fall back to his check downs. He wouldn't even wait for his progressions, he'd look to one receiver, see that he was covered (or believed he was) and then go to the check down. I remember it clearly to this day.
What we have seen from Peterman is nothing of the sort. No checkdowns.
Maybe Peterman will end up doing the same, but nothing that we've seen from him so far indicates that to be the case, until then, anyone who says that Peterman's brand of ball is similar to Trent Edwards is taking an amateurish take on the comparison, imo.