I think that 1v1 shows a single persons skill the best as you have to cover air and ground and work out your own counters without relying on a teammate. 2v2 does, as you rightly said, show how good at synchronizing builds you are and how well you can work in a team, but I do think that 1v1 shows how good a player really is.
Generally in clans, you would need people to be good at both, not just one or t'other because you don't want someone only good at 2v2 being challenged to a 1v1 and getting owned and making your clan look bad.:P