It's difficult to not come off as proud, since debates are often viewed as more of a battle than a pure exchange of information. Seems like it would depend on the person's demeanor.
There simply isn't a one size fits all for that sort of thing, however; I suppose it might be alright to say something like 'well, it's always a vigorous debate with you' and shake their hand in order to help ensure that no resentment builds if the other person prides themselves on their debating prowess. That sort of gesture could keep up an air of mutual respect, though it might also come off as corny if executed poorly or with the wrong sort of person. It's hard to say.
Would it be supercilious to thank someone for updating? I know I would feel uncomfortable doing it, but I often feel the urge to do so anyway.
There seems to be something vicious about thanking them. My own estimation of my own belief has not changed in these situations. I feel fairly satisfied that the other has considered my view and has shakily come to agree with it. I worry it would be a little like saying 'screw your opinion, now you see I'm right.'
However:
It is both rational and polite to thank them. The gentlemen's agreement of rationality allows for one person to be wrong and not lose face at all. When someone concedes something to me (a point) I typically feel the need to thank them.
What do you think?