After consideration, this is tougher than I thought it would be when I first read it. Mendenhall and Jones were your early picks and I'd go with them for sure early in the season, regardless of matchups. However, it's a little more difficult to choose between the other two.
I think I'd start Beanie over BJGE. Belichick isn't committed to the run and he seems to thrive on the Dolphins. He'll want to make a statement in the division early and will try to crush the Dolphins. I could see BJGE getting fewer touches than Beanie and the NE passing game going wild. Beanie is a question mark, too, but I think Carolina's DEF will allow him decent yardage and maybe a TD, as ARI tries to establish their running game.
So to answer your question, I'd sit BJGE.
Help with mine?
12 team, H2H, Standard Scoring (Starters in bold)
QB: P. Manning, Luck
WR: Julio Jones, Welker, Alexander, Hilton, Shorts
RB: Rice, Wilson, BJGE, LeShoure
DEF: DET, SD