The thing is... FFXIV is a PvE game, while Overwatch is PvP. That alone makes Overwatch a lot more competitive. The matches aren't like the raids in FFXIV, where you get 2 hours to kill the boss, and if you wipe you can just try again. In Overwatch, every time you mess up, it directly influences the end result. Whereas in FFXIV, all your mistakes are gone once wipe.

Now since PvP in FFXIV is... let's just say "not as much of a thing", a lot of the people who are after that feeling of competition that Overwatch offers, turn to parsing. They turn PvE into something competitive. Thus they are looking to do the best damage they are capable of.

So just like how in Overwatch you see people getting toxic because you are getting in the way of their win, in raids you will see toxic people getting mad that you might be affecting their parse.

But I still don't think it's at the level of how Overwatch is, since like I said - the games are very different.