You will occasionally encounter articles about how awesome full-frame cameras are. Lot of that is probably over-enthusiasm over a new piece of equipment or simple marketing, but it seems to me that at least these things are true:
The full-frame cameras are much more expensive. This is weird to me, since I had the impression that making electronics smaller is always harder, since you need more precise equipment.
That must've been even more important in the dawn of digital single lens cameras, many years ago.
So why was it chosen to make sensors smaller than is the film originally used in the cameras? AFAIK some lenses made for film cameras still work with some DSLRs, so why make the sensor different from the film?
Making large semiconductor devices with no, or only a very small number, of defects is very hard. Smaller ones are much less demanding to make.