From what I've seen bigger international leagues seem to be more lenient - may just be a sample size thing, as I follow NRL/Rugby/NFL and some soccer... and nothing else, to any degree - so I don't even get the big story headlines from other sports.
EPL is usually up to the club. Adam Johnson (convicted of sexual activity with a minor) was playing up until his trial started, I believe - and may only have stopped playing at that point because he entered a guilty plea and had his contract immediately torn up. Had he gone with a not guilty, he may have continued to play until it was resolved... not sure.
Not sure about other sports but NFL is case by case.. commissioner has a HUGE amount of discretion given by the CBA (waaaay too much). If the case was super public he'd probably land on the commissioner's exempt list (I don't think he'd even be paid in that case, but might be wrong?), otherwise he'd be free to play. But... I mean, the pressure would have to be significant on the league, as we've seen in previous cases (Ray Rice....). Even then, the punishment would likely not be anywhere near missing 2 seasons of play. Greg Hardy got convicted of belting the f**k out of his missus (on several occasions) and got a 10 game suspension (in a 16 game season), later reduced to 4 games. Messed up - guys have been suspended for as long/longer for weed.