Should I use nails or screws to refasten my subfloor to the joists?
Screws:


It doesn't sound like you're reattaching the entire floor; this is more like strategic intervals to solidify the fastening. Your nail/screw rate is not as important as if you were attaching a new subfloor from scratch.
Glue and screw is popular for more reasons than just rhyming
You're going through this effort to make it right. So do it right.