Undoubtedly Joe is a better traditional keeper than Willy, and I don't believe anyone on here has said to the contrary. Looking at the attributes that Pep now seeks, neither are exceptional but Willy was given the gig yesterday, that alone doesn't make sense to the layman.
I don't buy into Peps after match words yesterday regarding the keeper situation where he said today it was Willy, next time it might be Joe (or words to that effect).
Pep will have assessed Joe over a greater period than 45 mins against Arsenal (which is what a lot of posters are hanging their argument on for him not been given time), so it could be assumed that Joe can neither or is unwilling to adapt. Is there a relationship issue between the two? I don't believe there is as Pep is old and ugly enough to put such things to one side for the betterment of the team.
If Joe does stay, he must now realise that Pep will get his way and he will not blink at the thought of dropping him.
Pep coming is what we all wanted and now he is here, we need accept he is moving us in a new direction and there may be casualties. Of course we all surely feel sorry for Joe as he has taken us to this current level and (if true) he isn't to feature with us moving up the food chain, he will be gutted.