Difference between Burkhead and Lewis, White, Blount is that Burkhead can play on all four downs. I guess Lewis theoretically can but he's always hurt and isn't the kind of back who can handle 15-20+ touches a game when the plan calls for it.
"Starter money" is a pretty meaningless term when it comes to the Patriots. I don't think anybody expects Burkhead to be a 15-20+ carry bellcow, but the Pats clearly view him as a core special teamer who will also be able to contribute regularly on offense. If he can give them as good or better special teams production than Bolden did, while also playing, say, 20-30 or so effective snaps a game at RB, with the ability to be a threat both running the ball and catching passes...That could be a pretty valuable player to a team.