You usually play at the Xbox one, but the ping is always high and it hangs online. Then I connect the ps4 exactly as the xbox and everything runs like clockwork. Xbox connected again and the hangs goes on? What can this be?
Did you check the settings on both consoles? Otherwise I would reset the slower console times to factory settings and set up again.
See also whether on both consoles the current firmware is installed.
Otherwise, you could also look for the Xbox, have the experience that certain server just a bad load and I have some games at a certain time (in the evening in the US) worse Pings in Germany were available, since the servers were full.
