Oddly, my old Honeywell thermostat had way more problems than the Nest that replaced it. It would frequently turn on heat or AC and leave it on regardless of temperature. Replacing the batteries did not help. Replaced the thermostat and about a year later the new one did the same thing. Junk.
I chose a Nest for one reason. The job I had at the time involved lots of travel, sometimes with limited or short notice. I also live in a climate that gets very hot in the summer and *VERY* cold in the winter. A regular programmable thermostat is utterly useless in that situation as I didn't have a regular schedule to program. You end up either leaving the temperature set to whatever is comfortable all the time or else coming home to a hot or cold house. Since I got the nest 3 years ago, my utility bills have gone down 25% and I have the ability to, from my phone, turn off "Away" mode an hour before I get home and the house is comfortable when I get there. If I forget, it's no biggie and the heat or AC turns on when I walk in the door with no buttons to press or no manual mode switch to accidentally leave on.
I had a Nest for several years in an older house. It was pretty good and I only had a few problems with the 'charge by thermostat loop' power system it uses. But nothing that wasn't fixable with some extra wiring. That was right up to last year when it stopped heating at 11pm on a 20deg F night. I have to give kudos to Nest support, who was on the phone to help me diagnose it for about 45minutes in the middle of the night. Unfortunately, they gave me an option to try and run it, but sent me a replacement unit 2 day shipping. They said installed unit might not work and I may have to swap it out for another thermostat until the replacement came. It didn't work about 4 hours later and I had to swap the thermostat. I really liked the remote access, but I never did swap the new Nest they sent me back to that house.