Is there much of an adjustment for players to go from PL to another league Vs the other way?

We always hear about PL experience being important when a player is signed for your club (when you support one in the PL league). For my team (crystal palace) our new player Kamada is struggling with the speed and physicality of the league and is getting caught in possession a lot because he isn't used to getting closed down so quickly. He came from Lazio and Frankfurt before that. Previously Max Mayer had the same problem. We know it happens a lot to new players coming to PL clubs. But when a player goes to another league from PL do they have to go through a period of adjustment? Is it as hard?

When a PL player goes to Italy do they have to learn to slow their game down and not rush. Does lack of technical knowledge get exposed? When going to Spanish league do they struggle with keeping possession. Does lack of technique get exposed? Or does PL experience give them an advantage in any league?