How do I install fire blocking while finishing a basement?
OSB would be easier and faster, it gets installed BEFORE the top plate goes up. If you plan to use 2X4 framing set 1" away from the wall or if you follow the detail provided in another post, you can still use it as fireblocking.

When you layout for your top plate and chalk your line for setting the top plate by, before you do, measure over to sill plate that the joists set on for the dimension to rip the OSB. I would suggest to rip the OSB a little shy of the chalk line. that way you will always have it as a reference. My carpenters had ripped the plywood wide enough to cover the line to supposedly follow it but when the wall was finished framed it had a 1/4" bow in it.

Set the plywood, then the top plate, and build the rest of the wall.