Rage and Serenity from the soundtrack is practically a love theme for Charles and Erik because it's a combination of their own individual Leitmotifs. This essay explains in more detail what makes the piece so poignant.
"...at 0:42, a small melodic motif is introduced, which seems to generally be used as Charles' theme in the film. This continues to play as Charles acts as a mentor and friend to Erik, showing him the memory, and telling him to try again.
At 1:19 in the song, Erik's theme comes in. Now, Erik has two themes: a calmer, somewhat arpeggiated electric guitar riff, and a more intense "Magneto" theme, generally used when he is doing something violent. The one used here is the calmer one. However, instead of taking over the music entirely, the guitar actually plays the theme in counterpoint to Charles' theme, not sacrificing its unique timbre, but still blending in with the orchestra to create an amazing sound. The song builds to a climax as Erik finally moves the dish, and then fades away gently as Erik smiles and laughs, and Charles pats him on the back proudly.
This, more than anything, really enforces the metaphor that Erik and Charles are Rage and Serenity. They have their individual strengths and advantages, but they are stronger when working together to reach a single goal. And working together doesn't erase either of their individual qualities—Erik is still Rage and Charles is still Serenity, just as the guitar is still a guitar and the orchestra is still an orchestra. Together, they create something new and better, something more than a sum of its parts, as the popular saying goes. That's why the relationship between Charles and Erik is so powerful, and why this scene is so emotionally charged—they were practically made for each other, each perfectly complementing the other."
Hell, for that matter, James McAvoy and Michael Fassbender. While doing interviews promoting the film, they sang to each other and talked about how they would fly all over the world spreading love to the hapless populace if they had super powers. McAvoy even "confesses" that he and Fassbender have done the horizontal limbo.
Interviewer: What is the most common question you are asked?
James McAvoy: How many times did you have sex with Michael Fassbender?
Interviewer: That is the question. And what is the answer?
Interviewer: Extraordinary chemistry between you and Michael [Fassbender]. Can you talk a little about how you developed that onscreen?
James McAvoy: We had sex every morning, and that helped make the chemistry!
Interviewer: I know a lot of the fans loved in First Class the relationship between you and Mr. Fassbender, Charles and Erik, there was an intimate moment or two, there was a connection, do we finally get to see them kiss?
James McAvoy: (laughs) Air kiss. Air kissing and Eskimo kiss.
Interviewer: You know if you're air-kissing, he could use his weight to pull you closer.
James McAvoy: (laughs) It's good, he could try, certainly buy me dinner a few times first.
Interviewer: I know a lot of the fans [..] responded very well to the bromance, the masculine friendship, the intimacy that you shared with James McAvoy on the screen the last time. I asked him any chance of a kiss, and he seems willing if you're game.
Michael Fassbender: (sings) Sometimes when we touch, the honesty is too much... (laughs)
Interviewer: I'm welling up! That's an emotional moment.