Hello loaded question here..lol First each manufactures thermostat can and will work differently with different equipment. In the digital age algorithms play a big factor. Both the thermostat and the manufacture of the boards in the HVAC equipment. This will determine how accurate or sensitive it is. Although most are very close there are differences in model quality and functions you may prefer. All the manufactures you listed do make a quality thermostat, with that said some companies will offer better support and warranty on the thermostats, you will find Honeywell and White Rodgers are probably the biggest and most competitive and also work hand in hand with many of the HVAC manufactures. Example Rheem/Ruud tests with WR and now some Honeywell thermostats. Most manufactures do not test their equipment with thermostats they just use on and off toggle switches during development. ( odd I know ,but true) However I had a Robert Shaw thermostat hooked up to a Rheem furnace ( RGPH) in an old house and it was the most accurate thermostat to a 1/10th of a degree I ever used.
I hope I am not getting off track here to your original questions, as for the dependability I would stick with Honeywell or White Rodgers both have excellent quality and very good warranties. When choosing a thermostat keep in mind what features you like and the want to use them. Lux will not be a good choice here as they do things differently are seem to be a little more complicated in the set up procedures. But they do offer good web site help.
Lastly, what thermostat do I have, White Rodgers touch screen, I like the touch screen and the WR has a large lit blue back screen easy to see with my getting tired eyes.lol Much brighter than the Honeywell and in color. Let me know if this was helpful or if you have specific models your comparing. Thank you Richard