I've just joined this forum today so wasn't here to answer earlier. I just now posted this as an answer in another thread, but it's relevant here too:
Some months ago I bought an AF-P lens to use on my D7100, and ran into the same problem [as in the other thread]. It did auto-focus, but I had to re-focus after turning the camera on and off, or even after the metering turns itself off due to timing out. Following advice I found elsewhere on the interwebs, I updated the firmware of the camera - with trepidation, but it completed OK. After that the focus no longer reset up power-cycle. The D7100 with the latest firmware is ALMOST fully compatible with AF-P lenses. One cannot turn off the VR though - for AF-P lenses that's done via the camera menu but it's not available in the D7100. That does not seem to hurt too much, the VR on these newer lenses is pretty smart. And the lens I bought, the 70-300 AF-P VR, is a dream come true. Sharp handheld pictures at 300mm!
So to answer the question in this thread, I think the AF-P lens is much better: half the weight, very sharp even at 300mm, fast focus, extremely effective VR, and cheaper to boot. You may need that firmware update for the D7100 though.