The big dispute is from the players. From what I understand, the administration teams are on relatively good terms. Think of it as a school rivalry. The students of a school may completely abhor another school, but the teachers of that school could care less.
I don't know if you know the story of how the Hive came about, but I'll say it anyways. The owners of the hive wanted to make a server that had Survival Games, as well as other gamemodes. They came to Chad and offered to buy the server from Chad, seeing as it was the one of the biggest and most popular servers at the time. Chad declined because he thought the community was worth more than what they offered. The owners of the Hive understood his reasoning behind the decision and decided to create their own server; however, they warned Chad that since they were making their own server, their servers would be rivals to MCSG.
That's the basics of it anyways. There may have been bad blood when the two groups went their separate ways, but it has since dissipated. However, the communities, they took the bad blood and ran with it. The communities bashed horns for various reasons, such as: the issue of BSM, the fact that Variede left MCSG to help found the Hive, the staff of each server, even the quality of maps has been a cause for argument, but in my humble opinion, the main cause of conflict is the fact that the servers are relatively similar. The communities think "Oh, it's just like us, that means they're bad!" Now, you're completely free to think that, but frankly, that's a stupid reason to dislike something.
People love to argue. It's a simple fact. It's human nature. The communities will continue to fight until the day that the servers die. When they run out of good reasons to fight, they'll start arguing about petty things. The administrations will look at the communities with a touch of disappointment. They won't flat-out say to stop the fighting, but I'm sure they wish for it. If I'm wrong in anything I say, please tell me.
Thank you for your time.
~Lively