Re: Nexus 6 slowed down after Naugat update.
Did you do a factory reset after updating. Many say it's not necessary but I always have and did not regret it. Doing a saved restore is up to you. If I do a factory reset, I setup up the phone as new.
I would consider the reset if the cache wipe doesn't show an increase in speed.
One last point. N is expecting to see up to date hardware. The N6 has two year old hardware so this might be the case as well. My Nexus 6 is due to me today so I'll go through the process and post back if I have problems.