The two main differences are more armchair lawyering required to avoid fees (legacy carrier is often not going to put your bag in the dimension bin, but the Spirits and Frontiers of the world certainly will) and having to sit through three sales pitches instead of one on the legacy airlines. I think Delta is the only legacy carrier in the States that doesn't do obnoxious sales pitches - only the food cart upsell. Ryanair will come through with their hands out minimally three times since last time I rode them (though it's been several years, is it four now?)

One other difference I can think of is that carry-ons are more rarely included in the base fare in the budget airlines than the legacy airlines, though maybe that has also gone away since the changes where bags must be included in the listed price that Southwest pushed for.