I did both during my non-flying tour at KWRI in the 90's. Civilian was more interesting, more laid back, more challenging (tiny uncontrolled airstrip), and more expensive. I ended up switching to the base aero club. Less expensive, and I found flying in the military environment more familiar and comfortable. I enjoyed doing both, but $$ was the deciding factor.

Don't know for sure, but I don't think either way makes a difference to the airlines. You are much better off trying to find part time/contract work in something bigger than a piston, though.