Are Budget airlines tiny planes?

They typically use Boeing 737/Airbus A320 type planes. Which are mid-sized jets with a capacity of about 150 seats; give or take.

One thing to know about the European Airlines - although they fly standard large jet aircraft - the seating is a bit cramped. Typically because the flights are very short - 1 to 2 hours this is not a problem.

Easy Jet and Veuling for example are classic for those short people to freak when they are suddenly long legged. :o)

I'm 5'11 and have never had an issue with leg room on either Easy Jet or Sky Europe. But Ryan Air is a nightmare-total sardine class setup.

You can often determine the kind of aircraft that flies a certain route, on the website where you buy your ticket. I used to be a pilot (small aircraft not major airline), and among pilots the feeling is that ANY Boeing or Airbus aircraft has a very high level of aircraft reliability and pilot competence. It is only when you get into the smaller aircraft that safety issues may possibly be different. And statistically it is true that very small aircraft are more dangerous, although accidents rarely happen.