I have 2 Nest Thermostats and while I am not sure it saves me any money (it may) I use the app all of the time to turn just the fan motor on. Especially when I am in the Theater room with the doors closed it really circulates the air in the house instead of freezing the rest of the house to cool down just one room. I am sure the Ecobee does the same thing but that feature alone makes it far superior to a normal thermostat (and I can do it from my phone or my Home theater remote)
Jamie