Whenever I played the games at around the same time as a friend I would try to choose the other version than the one they're playing. That's the way I chose the version for the Gen VI and VII games, so Y, Alpha Sapphire, Moon and Ultra Sun.
I also sometimes have played the games with walkthroughs or let's plays for company, and then I would choose the version that's not the one those people are playing, as well. Those were the ways I chose the versions when I played the Gen V games, which were Black and White 2, if I remember correctly. I've done this when replaying some games as well I think, but I don't remember any particular examples.
Before that when I was younger I used to go with the cover that looked cooler to me, or had the Pokemon I liked more. With Gen II I played Crystal first, if I remember correctly, because it was the third definitive version, and then I don't remember which one I played first between Gold and Silver. Then with the rest I went with Ruby, LeafGreen, and I don't remember whether I played Diamond or Pearl first, same with HeartGold and SoulSilver.
Nowadays it's a combination of all those criteria, I guess. I come into the games with the idea that I'm going to be replaying them at least once, anyways, so I will play both versions in the end, so I don't really think about it too hard. I'm currently playing through Shield and I still haven't decided which version I'm going to be playing for the Gen IX games. For the Let's Go games and the Gen IV remakes, I'm not 100% sure yet, but I'm thinking Let's Go Pikachu, because it reminds me of Pokemon Yellow and that may be nice for the nostalgia, and then Shining Pearl, because I like Palkia slightly more than Dialga, and from what I remember from the last time I checked, which was a long time ago, I liked the exclusive Pokemon slightly more from Pearl.