So if they really commit to one guy going forward, I feel like it makes more sense for it to be Zappe at this point.
Jones had his opportunity to respond tonight and dropped the ball. The fact he was pulled so early tells me Belichick was prepared to bench him for performance reasons, which means the leash was shortened coming into tonight. The fact Belichick was thinking that way should say a lot.
Here's why sticking with Jones presents a problem IMO:
Should Jones continue to play poorly, you're really stuck with him, barring benching him (again) which would create another fiasco, not to mention walking back your commitment to the team that Jones is the guy for the time being.
Jones had issues early in the season, got time away due to injury, returned and those same issues picked right back up like they never missed a beat. If you commit to Jones and these issues don't go away, and the turnovers, poor pocket awareness and field vision all continue, you're really in a tough spot because he's close to unplayable right now with the turnovers.
If you commit to Zappe, you get someone that while limited and lacking in experience, hasn't demonstrated repeated struggles throughout the season. Given his limitations (and strengths), I get the sense you have more upside with Zappe right now and can build around the things he does things well. You can work with altered release points, throwing angles/windows/lanes, play-calls/route-combos to hide those flaws. On the other hand, if your QB simply isn't feeling the pocket well, nor seeing the field well, and is turning the ball over, you can't game-plan around that, I'm afraid.
Basically, Jones has been making repeated mistakes. He had the opportunity to respond tonight but continued to have the same problems, leading to him being benched (which didn't happen in the moment ; Jones being benched was certainly settled upon as a possibility in advance of tonight's game, for it to happen so quickly after his struggles tonight). Making a commitment to Jones for the the foreseeable future and having him continue to play poorly creates a really tricky situation.
On the other hand, Zappe has not made repeated mistakes. His game was exposed tonight, no doubt - he has limitations and flaws he must work on. But, I didn't see repeated errors, and many of his positive traits - pocket presence, poise, accuracy, arm zip - were all still present despite some of his newfound struggles. If you roll with Zappe and he stinks it up, it feels a bit easier to say, "OK, Jones, give it a whirl again" than vice versa, considering how this has all transpired.