Just a general question regardless of camera types.

So which is the better way to go for a camera body FF (full frame ) or cropped?
I understand that FF lenses won't work on a cropped body as such, at least not without doing damage, whereas I have been informed that it will work the other way around.

What is the basic difference in image quality and types of uses? Is there specific fields for each type of body and lens combinations?

Cheers