While I normally reboot all my devices at least weekly, I just noticed that, as of right now, and probably since I got the 5.1 update, my Nexus 6 has an uptime of over 624.5 hours, which is over 3 weeks. Color me surprised. My N7 2013 LTE crashed in the middle of doing stuff Thursday night, again with 5.1, so... I guess the N6 wins, in my book, for right now.
As reference, whenever things get really wonky, and nothing else works, I power the devices down (as much as that pains me as a *nix sysadmin), and it seems to fix the problems. 3.7 weeks (and counting) seems to be an amazing run for current hardware/software combos.