I consider the FF programs, elite benefits, and the miles themselves as part of the package that I'm buying - along with the schedule, routing, price, and other factors. Therefore, I view the programs as simply another piece of the competitive puzzle.

For example, even though AA is my favorite FF program (because it is the only one that gives me lifetime elite status), my last two trips have been on YX and WN. All of the cities involved had AA service, but YX and WN were competitive in other ways, so I passed on my preferred airline to fly two airlines on which I have few miles/credits. My next three trips will be on AA, because the fares/connections were roughly equal, and AA Gold status was the difference-maker to ensure that all of the trips are on AA.

So I would say that FF programs are certainly a competitive tool - how high you prioritize them against routing, aircraft, service, and fares varies person to person and trip to trip.