I am with jlb71 on the Kyoto-Nara trip, unless I had a valid JR pass (and I wouldn't validate one just to include this trip), I'd go by private rail. While the private rail station is closer to the sights, it's only a block closer, so that's not the reason for me. There are two other reasons:

1. A regular train on Kintetsu is cheaper than JR.

2. If you want to do a minor splurge, the Kintetsu line has fairly frequent limited expresses on this route that are more comfortable than JR.