Changes at WR, Oline, and Special Teams helped, so did playing the Jets, but the eye test is what matters. Barkely visually is just much better than the 3 quarterbacks the Bills have started this year. He is talented and polished. Allen is talented and unpolished. Anderson and Peterman had moments where they looked ok for filling in for a few downs or plays but never could not put entire games together.
If Allen wasn't coming off a long layoff I think he could fare ok. He has not seen a live defense in a long time. Starting him makes little sense. I would just go with Barkley until the Jets at home. If the goal is to give him reps and confidence then the Jets at home in a few weeks looks like a much better spot to return. If Barkley beats the Jaguars and Dolphins you just have to stick with the hot hand until they are eliminated from the playoffs.