According to the Dartmouth website, the first year cost of attendance (which includes tuition, room and board and student fees, but not books and supplies, health insurances and miscellaneous) is $66,579, which is essentially the same as Wash U. http://admissions.dartmouth.edu/financial-aid/cost-attendance/cost-attendance
That means that Wash U will be $5000 a year cheaper than Dartmouth.
Given that you’re not sure about Greek life, I would pick Wash U. It’s cheaper and Greek life is less prevalent.