Is Application.persistentDataPath consistent on consoles?

Does someone know if Application.persistentDataPath is equally consistent on consoles as it is on PC/Android/iOS? If it is not, how does it work / how to make it work properly on consoles?

In short, no - consoles tend to have their own filesystems and requirements, and each is handled differently. You would need to handle each platform separately yourself (maybe with some generic wrapper) however that is outside the scope of this website and these are more questions for the platform-specific dev forums.