According to Lowes, ecobee's new thermostat (ecobee Smart Thermostat Premium) has built-in z-wave and requires a hub

I would recommend the 2GIG z-wave+ v2 700 thermostat or the GoControl zwave+ thermostat. Both of them provide fine-grained, deltaT based, control over multi-stage equipment. The control offered by these thermostats permits, for eg. optimizing 2-stage cooling for either temperature reduction or dehumidification. This is the same type of control offered by ecobee, or Honeywell’s higher-end WiFi thermostats.

In contrast, Honeywell’s zwave thermostat relies on the number of cycles per hour (CPH) equipment has been run for. I had one of these for 2 years, and was unable to achieve the same comfort levels I had with the ecobee.

There are several threads on this forum between @neonturbo and me trying to figure out a reliable way to convert between CPH and deltaT. Finally, I gave up, and got an unused GoControl from a fellow forum member, and installed it. Within a few days, I was back at the efficiency and comfort I had with the ecobee.

OTOH, if your HVAC equipment is just single-stage, any zwave or zigbee thermostat should be fine.