Yes this is it, I believe.
Puig is trying (needing) to prove himself - most often it works out, but he misses too often right now I'd agree. I think it's mostly about him forcefully attempting too much rather than him being technically subpar.
A 16/18 year old is in a totally different stage, more in need to show he can circulate the ball well and not make mistakes (Gavi made at least 2 big mistakes today though, giving the ball away unforced).
Remember, the 60mins or so that Gavi got today is more than what Puig has gotten the last year bar just a couple of games... Not only is the carreer stage much different, it's different to arrive from the bench with a few minutes or so, and in a competitive game...
From what I've seen of Gavi so far (includes a youth game where he was the star of a losing Barcelona) he is a bit too conservative, and forces things a bit too little, but he can surely change that and is already superior to someone like Pedri in his movements and general understanding of the game, I feel. If a player with the vision of Gavi just gets to play the opportunities will arrive, he doesn't need to force things.
Overall, I much prefer a player who keeps the ball safely too often to a player who tries and fails too often. I think both Puig and Gavi can play very well for Barcelona A this season, and it's just minor psychological tweaks that I'd like to see in their games - they both have the qualities needed.
Yeah it is more of a mentality thing. From a technical standpoint, its a toincoss between the two. Still behind Pedri tbf, but not far by any means and again, it is just down to confidence/match fitness.
Especially with Puig, I give him the benefit of the doubt a lot because I see why he plays so risky like you said, trying to prove himself to Koeman and get minutes but the better thing in this situation is to show maturity in your play and know when to kill vs. when to play safe. From a hardman perspective like Koeman brings, I can see why he gets annoyed at times but I still feel he is too harsh on the lad. Its a bit like Thiago early on here, he showed the same class but sometimes had sloppy turnovers trying to do too much to force his way in against Xavi and Fabregas.
Puig just needs to demonstrate that balance between control and output and as long as that is happening, he should play. Thats why even when Gavi and him turn the ball over, its ok because they bring positive production overall. Its ok to turn the ball over here and there when you are scoring, assisting, creating and dictating play.
The problem comes down to Koeman being able to balance the playing time of them all. Gavi should probably be a B-A floater while Puig needs to be rotating for Pedri a lot more and in certain situations, I would like to seem next to each other in the MF. It is just Coutinho, Pjanic and Roberto are all on ridiculous wages so if they are still in the mix, it is going to complicate Koeman being able to give both Puig and Gavi the minutes the deserve down the line.
That is why I sorta see it as an either/or situation sadly between the two, unless we lose at least two of those big name MFs who are on these high wages.