Internationally it can sometimes make a difference. With Asia routes you might get some of the lowest fares from the likes of EVA, China Airlines, Korean, or a few others that don't have very useful miles. Icelandair could be an example for Europe.

Domestically the legacies all tend to charge roughly the same, with the difference possibly being due to extra taxes from a connection instead of a non-stop. If there's a ULCC in the mix like Spirit the legacies probably won't match (but will be pulled downward) because Spirit goes farther with the feeing frenzy.

Spirit, BTW, is a good example of a FF program that does NOT give much incentive to fly. You get only 50% miles on lowest fares, expiration is aggressive, and point accumulation, mileage sales and avoiding expiration are mainly done through the credit card (if you can get). You're not really rewarded that much for flying.