During the 20 days it took me to figure out which airline I wanted to be comped on. I had to figure out where and how I would be flying. Since I live in the DC area, all the major are accessible to me, and BWI provides the SW effect on pricing. I'm a leisure traveller which means lower fares almost always prevail. I don't mind sitting in the back, but do like having my pick of good seats in Y. My flying pattern for the year post-what I've already booked is a few transcons, some up and down the east coast flying, and probably 1/2 transatlantic flights. So with that being the case CO came away as the best airline for me after leaving DL (which was hard to do because their inflight crews are so good. CO comped me with no problem to their Silver status, (same as I had on DL.)
Strategy as to who to get comped on should definitely go down to where you're going to be flying and how you're going to be flying there. It also might not be beneficial to get comped on everybody at once. If you decide you don't like the carrier you've flown most of your 2003 miles on, then the others likely won't comp you again.