i think both of you were behaving like little kids. the videos probably show only half of what is done. I think the best option is to make them join a ts with an admin and talk about it, like you would do with kids. if you start banning, one of the two will feel like the admins are choosing side, while the other one wont stop bragging about it in-game. both sides have to stop this childish behavious.
thats how i would look it at it objectively and how i would handle as somebody with a position of power (in this case it would be an admin or the leader of a clan)