I had both and decided to stick with Ecobee. The nest was too smart, it kept switching temps when I didn't want it to and wouldn't switch when I wanted. The ecobee is just as easy to install and in some systems is easier. My system only had 4 wires with no 5th "common wire" to supply constant power and using the nest it completely shut down twice. The ecobee has an additional unit that allows you to wire your system so it supplies constant power and has been trouble free since installing.
I also really like the additional sensors the ecobee has. We have 3 dogs and the Nest ignored them and kept turning the heat down when we both left the house so my poor small dog was chilled when we came home from work. The ecobee sensor can tell when the dogs are in a room and turns up the heat on that floor.