@Sparks
Guess what I'm also doing?
Like @Lisse24, I have fond memories of RfK. AJ was a player that used the social roll system for everything. ("Greetings! I am (rolls dice) happy to see you!"). And that often led to amusing results, especially when he and Cai (my PC) were bowling. (Yes, my Ventrue liked to bowl, go fuck yourself.)
My combat system is very simple. First, you have one of three positions on your side of the battlefield. Second, you have a limited variety of attacks. Third, you have some talents and tricks that be used to tip the battle in your favor. Finally, you have Drama Points to spend and thereby increase your chances of success. You get a set number of Action Points per turn, and people act according to an Initiative Order set at the beginning of the entire combat (it doesn't change by round). The objective is to be the last squad standing.
Social combat would be the same. First, you would have one of three approaches for your side of the debate. Second, you have a limited variety of arguments, jibed, and quips to make. Third, you have some talents and tricks that be used to help you achieve your outcome. Finally, you have Drama Points to spend and thereby increase your chances of success. You get a set number of Action Points per turn, and people argue or insult one another according to an Initiative Order. The objection is to be the last person/group with any credibility.
So, I'd limit social combat to large scale debates or situations where the PCs are trying to achieve some sort of social objective, like negotiating or bargaining to take the lead on some campaign. I don't think it'd work well to hammer someone's social standing (essentially, PvP).