I want to ask the question in two parts,
(1) Is there some fundamental distinguishing property between Abelian and non-Abelian Cayley graphs? (say some specific proof technique which distinguishes them?)
(2) Are there any set of (constant degree) (Abelian) Cayley graphs which are expanders? Do they have any distinguishing property?
For reference one can see chapter 5, starting on page 30 of these notes, http://www.eecs.berkeley.edu/~luca/books/expanders.pdf