Williams is about 20% bigger than Davidson. (Williams has over 2100 students, Davidson only 1700.) That may not seem like a big difference, but if you were to take away 400 of Williams' students, I think you'd notice.
Demographically, the schools are a bit different, too:
Davidson has 4 % international students; Williams has 7%.
Davidson says they have 14% "students of color."
Williams has 29% "U.S. minority enrollment."
Williams College :: About Williams - Fast Facts November 2008 Davidson College - Fast Facts
(you can check my numbers on these links)
Davidson has fraternities and eating clubs; Williams has neither.
My sense is that Davidson has more politically conservative students than Williams has, but I have never seen any figures regarding the political leanings of the students at either school.
At one time in the '70s, Davidson referred to itself as the "Williams of the South." The schools are similar in many ways (both are very academically rigorous and have first rate faculty) but I think the differences in size and diversity are significant.