My son graduated from DC last spring and my daughter graduates this spring.
Greek life at Davidson is limited to fraternities. There are no sororities, but the women have eating houses/clubs that substitute.
My impression is that, as you'd expect, each of the fraternities and eating house has their own personality, some more distinct than others.
Its also my impression that fraternity membership is not overly competitive but every house may not be a fit for you and you may not be a fit for every house. You still want to choose wisely and so do they.
Membership in the eating clubs is sort of a self-selection process with a little bit of lottery thrown in. Its not a competitive "rush" situation.
The "structured" social scene at Davidsion centers around Patterson Court (the physcial location on campus where the fraternities and eating houses are located (all non-residential). Almost everyone lives in the dorms and on-campus apartments. Fraternity and eating house members tend to congregate together in the dorms. But I think you can have a perfectly acceptable social life without joining one.
I hope that helps.