GSP is my home airport.
Priority lane/access is my first priority. Then free checked bags. Then award tickets. Interesting note about the free checked bags: they help me justify a Delta flight when AA is cheaper, as I can say "I'd be paying $xx more for my bags on AA" (and I'm not using that as a lame excuse, I often do need to check a bag - or even two sometimes ).
Where I fly to in the US varies a lot: Texas (SAT, IAH, HOU, ELP - AA has definitely an advantage for Texas), PDX, DEN, COS, MSA, EUG, MCO, SMF... and more to come. Only one flight per year across the pond to Europe (usually to LYS).
beachmouse mentioned the hub's, that's a good point: with DL, I go through ATL (almost all the time), DTW, SLC, and LAX. LAX kind of sucks (but it's an AA hub too anyway), but the other ones work rather well compared to most AA HUBs. @
wetrat0: surprisingly, for my routes, DL and AA actually offer some similar schedules and connections. But going back to the hub's, I'd much rather fly through ATL, DTW, and SLC than through CLT and ORD.
When I look at my frequent-flyer colleagues, those flying Delta seem to experience trouble less often than those flying AA.