I have the Priv and have used the V10.
I found the V10 to be more unwieldy than the Priv (but that's something you can adjust to). I don't like fingerprint sensors, so I didn't really use the one on the V10. Some of the features in the V10 camera were cool and I liked them, but day-to-day the main cameras on these phones are comparable. I only use the front camera for Skype, so the low specs on the Priv front camera were not an issue for me. I also like the PKB, and the Priv is really your only option for that. Software was a wash, but I do appreciate the monthly security updates on the Priv.
That said, I felt that the V10 had the more solid construction and while I had no build issues with the Priv, it didn't feel as solid. The slider mechanism also concerns me a bit, as moving parts can easily fail.