Desert Trails is in Tucson at a lower elevation than Benson so it will be a bit warmer.
Desert Trails is good if you're a hiker with easy access to trails. It's more rustic.
Butterfield is not quiet. It's along a busy road, Safeway grocery is next door and you'll hear the train... all hours.
I would think Butterfield would be more expensive but I don't know. I've not stayed at either but know folks who have. It just depends what kind of surroundings you enjoy.
Cochise Terrace in Benson would be more quiet.
Personally, I wouldn't lock either in before experiencing the area. If this is your first time in Arizona I'd suggest trying out different areas a short time before committing... and not just Arizona - any state you are looking for long-term.
Full-Timed for 16 Years
.... Back in S&B Again
Traveled 8 yr in a 40' 2004 Newmar Dutch Star Motorhome
& 8 yr in a 33' Travel Supreme 5th Wheel