If Neymar Jr goes to Barcelona I think he will be able to perform better than PSG. Because the players of the Barcelona team have performed exceptionally well at the moment. If Neymar joins the team, the team will be even stronger.
Neymar hasn't performed bad for PSG, his scoring statistics are good and among the best the league has seen I think. His issue is how often he is injured and how much he wants as a salary. If he is free of injures and in a good physical shape, he can help any team no matter whether it is Barcelona or some other top team. But is a player worth the money when a coach doesn't have the slightest idea about how many games the player will be able to play?
Yeah the main problem for Neymar is especially his getting injured quite often and for long time periods at the same time. Maybe his statistics have always been impressive at PSG but he can't make the necessary contribution as long as he continues to get injured like this. There is no reason for PSG to pay a high amount of money to him while he is in this condition.
When it comes to Barcelona I don't think they can sign him this summer. There is just no way to do this unless they sell some players first. Maybe they have a big amount of budget but it just doesn't end there. They need to act according to La Liga FFP rules if they don't want to be punished.
But I don't get why the situation should be any different for Barcelona regarding Neymar's injuries than it was for PSG. Whether they can sell a lot of players or organize some sponsor to pay the salary, it is currently said that they want a club from Saudi Arabia to support the deal or something, they would still have the same issues that Neymar could be injured after two weeks in the season and then miss 12 weeks of the season and then play again for two weeks and get injured again. I don't think he is worth so much money.