Monolithic Reference Collection, vs Per Paper Reference Collection, or Both?
I usually go with a single database, arranged in folders and/or tags. So the references are present one time, and then I just move them around according to what I need to do.

If you have separate databases, you risk to duplicate records, and save the same reference many times.

This also depends on the type of system you use: Zotero and Mendeley (the tools I mostly use) go with the single-db solution arranged in folders and tags, whereas EndNote allows to create separate libraries.