By saying Troy Brown-like, I mean the "little engine that could" that exceeded expectations and was committed to the Pats as a team while playing in New England. A player, like Tom Brady, that earned everything he was given in the NFL, because he was not the rookie heir apparent and fought for and earned a place in the NFL despite teams passing him over.
You cannot compare Welker and Brown because they played on very different Patriots teams with very different issues. Every athlete has an ego (not sure how you can compare athletes there, absent "get the ball to me" even when it is detrimental to the team) as competitors want to win and want the ball, metaphorically or literally, with the game on the line. While Troy Brown played defense as a WR, Welker, to my knowledge, was never asked to assume that role. Welker was about as versatile as they come, so I am not sure where that basis for comparison arises.
Team players do what they are asked to do by the coach, and do so without complaint. Brown is soft-spoken, Welker is an extrovert and a comedian. There is neither intrinsically wrong with either. I don't know how you compare "off the field."
I don't think you can compare them as to how much they meant to the Pats, as both were a huge part of Patriots' success within their respective eras.