I took out my passenger side rear axle. I turned the axle in my hand and the bearings felt perfectly smooth. The one I was going to put in also felt perfectly smooth, but it was stiffer than the one I took out. What I mean is that when I spun it around, it wouldn't go as far before stopping. Which axle should I put back in, the stiffer one or the looser one? Also, do I need to use axle grease?

With these bearings, "stiffer" is better. I base this on the fact that new ones are pretty tight & stiff when you get them.

These are sealed bearings and come "pre-lubed" so no extra grease is needed on the bearing but put a little grease on the seal surface.
DD