My favorite has always been Karkat and Kanaya, just because I've always related to each of them and their struggles the most. I think they are both some of the most relatable characters in the comic when it comes to maintaining relationships or not really being in one at all, and getting into one for the first time. One of my favorite Karkat conversations is actually when he's talking to Terezi during the walk-a-around Dancestor portion after she meets Latula for the first time and is like "Wow, my Ancestor is so much fucking cooler than me :/ I haven't accomplished much of anything in comparison..." and Karkat is like "Bro wtf are you talking about please stop comparing yourself to a dead girl you just met, you're better than you realize that's just your insecurity speaking and also you're like my best friend I will not believe you're worse than someone else."
I liked it because Karkat has always been one of the trolls that are significantly weaker than the others, but he's still hung around anyway, just because he cares a lot about the others and maintaining a good relationship with all of his friends. He's not the best at other relationships or Quadrants, but he's literally one of the best friends I think any of them could have asked for, and I think that making him THE friendship troll was the best choice that they remembered, even during the whole Epilogues situation lol.
And Kanaya's struggle of wanting to be in a relationship where she's not someone who has to coddle and help two other people, and then choosing Rose because, for the first time, she's someone else's equal, and not being put in this "mothering" role was also really relatable. I feel like what makes her so great is that she's someone who's a lot stronger on her own and who can make good decisions when she's not inundated by the need to enable other people's bad habits and wants. She's a person who's capable of so much more than just being "The Mom Friend," like being an actual good leader. My favorite Kanaya moment was actually when she knocked Karkat out after they left Echidna lol, because she knew letting him fight would've resulted in him just dying in the end like last time, so she decided to not enable his want to prove himself in battle or whatever and protect him.
I always liked their friendship in Beyond Canon because in the end they're the last two Trolls from the original group who are still dealing with the rest of the world, and sure that sounds awful but I think that's for the best and that its something they'd both want because they wouldn't want their friends actually to have to deal with a whole war. I mean, Sollux calls Karkat up for food (lmao) and Karkat is more annoyed that he's calling during an active battle than that Sollux isn't "helping" out or whatever T_T.