Some of both - I used to have a few shoeboxes sorted by color...sort of. BLue/green/purple in one, black and white and grey in another. I found out (a) if I'm going to do it by color every color must have its own box and (b) clear containers are better so I can SEE what I've got.
All my strings are in one container together. I have some 1.5" squares together and some 2" squares together.
But most of my scraps are mixed up in one big box. I'm slowly collecting the clear plastic containers that my dishwasher detergent packs come in - so far yellow and green have their own containers.