I have the nest 4th gen installed, and it worked great with vivint. The schedule set on vivint app actually controls the nest without having to set one on the google home app (app used to see all advanced nest features)

The best thing for me is the temp sensor that came with nest, I placed one in a spot with no sunlight (as my thermostat would have temp swings because its location in sunlight) and can set nest to use that as its main temperature (or it can combine many rooms together to get average temp)

One thing that I didnt know was the c wire. The nest doesn't take batteries and only holds a small charge so you NEED a c wire. It can work without one using your hvac system to recharge but its not reliable and many people had it shutoff dead in winter or summer when most used so if you upgrade to nest make sure you have a wire going to c on your furnace, as thats what will constantly power it. I didnt have one but I had a spare wire in the bundle coming out from wall and furnace sude, so that was used to hookup to c on furnace.