We all simply adore our best friends and our boyfriends and we think they when they meet they just might hit it off but sometimes, things just don't work out. It could be a personality clash or your friend could really be seeing a different part of your bf and vice versa.
I think what you should do first is think if there is any truth in what your bf and best friend are saying about each other. Why don't they like each other? Is it something superficial or could one of them be seeing something you are not? Think about it objectively.
If you feel that there is really nothing wrong with either your friendship or relationship, sit them down individually and tell them that you have evaluated your friendship/relationship and you feel that there really is nothing wrong. And you understand that they might not hit it off but you would appreciate it if they left you to evaluate your own friendships/relationships.
The best thing you can do really would be to not talk about your bf in front of your best friend and vice versa. I used to keep my relationship fairly separate from my friendships because well, they simply do not overlap.
And I think that is the best thing you can do. Be firm when talking to your bf and best friend but be nice. And this situation is making you miserable and tell them if they truly loved you, they wouldn't want to make you upset would they?
Just talk to them hon. Good luck.