I wouldn’t call myself a frequent flyer, but I fly at least several times a year, and I’ve taken a lot of different airlines. To your point, I honestly haven’t seen much difference in terms of cancelation or delay between budget and regular airlines. There are 3 main differences in my mind.
First is that budget airlines nickel and dime you. Carry-on isn’t free, it’s an add-on. Your backpack size is thoroughly checked. And if you mess any of that up and they catch it, the upcharge is huge.
The second point is sort of a continuation of the first: on-flight service. Depending on the duration of the flight, non-budget airlines will give you some snacks and drinks for free. Budget airlines charge you for them. (I once had a budget airline try and charge me for water when I was fighting off a headache…) Some of the nicest airlines will even have entertainment consoles built in to the seats, even in economy.
Third is seat space and comfort. The seats on the nicer airlines have noticeably more leg room and more cushion. A lot of them have adjustable headrests and recline a bit. Sounds like a small thing, but I have pretty long legs and a bony ass, so it makes a huge difference to me.
For shorter flights/trips, I’ll still do budget airlines sometimes. For longer flights or if I have a lot of luggage, I usually have a strong preference for the nicer airlines. Of course, depending on how big the cost difference is, I’ll occasionally go against my preference.
Unfortunately sometimes it’s really hard to avoid. I’ve been to restaurants that don’t even have physical menus. You could probably find a menu on their website, but not always.