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.