Cone wrenches or a (thin) adjustable wrench?

Hey gang. I'm building up my bike repair tool set, and it looks like I'll either need to get a set (or several popularly sized) cone wrenches and/or an adjustable wrench with a thin profile.

I figure an adjustable wrench could help service anything from axles/hubs to headsets, which cone wrenches are limited to the size(s) you've got.

Any advantage/disadvantage of one over the other that I might not realize?