I currently am employed with ASA as an f/o online for almost 4 years. I'm still looking at another 6mo+ before I get the opp to upgrade.
If it were me (obviously it is your decision), I would take the ASA offer first if it comes, then consider leaving for Chautauqua if they call. Why? PIC time baby....
If you are looking to move up in the Majors in the next few to several years, you really want the quick upgrade.
Don't get me wrong, with all of the little problems and without a current contract (4 years in the making), ASA has still been very good to me. I enjoy the flying and my fellow pilots.
I say this because ASA has seen little to NO growth in the last year (we were also bidding on the Continental flying lost from XJT and lost to Chautauqua). CQO has grown quickly and offers the quickest upgrade.....
My .02 worth......