I used Ecobee3 for a few weeks and had a good experience except for buggy smart home (ultimately had a very bad experience with their customer service, simply awful as they did not want to replace my device and kept blaming me). For a quick comparison and why I think Ecobee is a better device overall:
Ecobee has more functionality, like you can schedule vacations in advance, scheduling is easier, setting comfort profiles (home, away, sleep) instead of temperatures which makes scheduling a lot easier. Learning is kind of nice with Nest but does not seem very useful unless you have a set schedule that you follow every week. I like how on Ecobee the screen stays on all the time so you can always see temp without having to get within line of sight of it like Nest. Also Nest seems to overshoot heating the house, like I’ll set it to 70 and it’ll heat until 72-73. I spoke with Nest support and they said this was normal.. ok… Ecobee didn’t do that. Nest does look better for sure. Ecobee is plastic while Nest is stainless steel, but besides that I can’t think of anything Nest does better. I also kind of miss the remote sensors because our upstairs does get more warm than the downstairs, which is where the Nest is, and with Ecobee i had sensors upstairs and it factored those in (or just used bedroom sensor during sleep mode). Lastly, kind of unsure about the future of Nest, seems uncertain, whereas Ecobee is coming out with a new device soon. But really my customer service experience was so bad with Ecobee that I don’t know what to do lol. I’m edging toward trying again with Ecobee though once their new device comes out. Nest really seems dated.