PL games are in "arcade mode", meaning that none of the effects of the private league have any influence on your players -- minutes, injuries, etc.
PL games are beneficial in that they can let you compete with friends on a "bring your best" footing, as you don't have to balance PL minutes against league/cup/scrimmages. They can also allow you to try out new tactics with your "A team", as they will use the same game engine as the league matches while the minutes don't count toward your weekly total.
There is no financial or other benefit to PL games.