A mixed bag of lollipops
My Nexus ran like something brown and steaming after the upgrade to Lollipop. I went back to 4.4 and it was fine again, next tried the 5.02 update and it ran ok'ish but web browsing was a 5 minute page loading affair and any memory intensive app ran like treacle so I yet again downgraded.
After being nagged for a long time to update to 5.1 I was pleasantly surprised. Most performance issues are gone apart from the memory leak others mentioned. It's crazy bit I can have everything force closed, turn it off overnight and have problems running an app when I turn it on from sleep overnight. Then I force close whatever app I tried to start and it runs superb for several hours, even Chrome or Firefox. It seems that as long as I remember to close apps after I get to 4 or 5 running in the background then it's happy, except for the memory leak after a few hours of non use.
Strangely my new Moto E 2015 runs Lollipop 5.02 and it's a dream, even with a ton of apps installed. Literally runs like silk and makes me wish it ran so well on my Nexus 7 2012.