It depends a lot on how often you fly - I prefer Skyteam partners (ie, Delta in the US) whenever I can because I fly often enough to have award status with them, meaning lounge access, priority support, upgrades in-flight, etc... I'm sure I pay them more raw dollars than I would if I booked my trips on the absolute cheapest airline in all cases, but the perks make all the difference between the flight being a chore or a moderately pleasant experience.
I have plenty of friends, though, who don't fly as often as I do and can therefore chase the cheapest fare. It doesn't matter to them if they get a flight with an airline they don't have status with, or an airline with no special perks at all, because they're not on the road often enough to qualify for those things in the first place. Raw price wins.
Travel is one of the few industries where brand loyalty still has some tangible perks (albeit decreasing every time airlines revamp their rewards programs), so especially within the US where pretty much all of the airlines fly to pretty much all of the major airports, its an approach worth considering.