The main difference is that the low-budget in EU is much more aggressive, to the point where IMO there's not much sense in racing to the bottom with them; you'd never beat them on cost. And European consumers are more willing to put up with crappier flights because (Western) Europe is so much smaller; Lisbon to Berlin is under 4h. Plus the high speed rail is available as an additional competitor, so national airlines have to differentiate there as well.

The major American carriers mostly compete with each other and Southwest.