I lived in Murphy for three and a half years from June 2001 till February 2005 when I moved to Hiawassee, GA. Personally, I'd choose Burnsville and I haven't even been there.
Murphy is in the very far western part of NC, and the further west you go, the less developed the towns are. There is a very small medical center and I'm not a fan as far as the choices in doctors. They don't get the brightest and the best.
Keep in mind that if you get into a serious car accident there, you'd have to be air lifted out to get critical care.
The altitude is Murphy is below 2,000 feet (not counting the surrounding mountains)
and that means hotter summers.
Murphy is very spread out as far as housing. For groceries, you have Ingles, Wal-Mart, and a couple of other unimpressive stores that few people go to.
The school system is okay. There is an outstanding
school system in Hayesville, which is to the east of Murphy. The land in Hayesville is more beautiful, but it's even smaller than Murphy - tiny really. They do share gorgeous Lake Chatuge with Hiawassee, GA though. The lake is centered on the state line of NC and GA.
Snow - it will snow an inch or two and usually melt in a day a few times in the winter. You have to watch it if you have a steep driveway, because you get ice a little more often.
Murphy's downtown was kind of betwixt and between when I first moved there. It wasn't a place to kill time or draw tourists, but several businesses have recently made it more inviting. It still isn't what you'd get in mountain towns closer to Asheville though.
You are in close enough proximity to Hiawassee, Blairsville, and Blue Ridge, GA if you need to expand your horizons. The best restaurants are in Hiawassee and Blue Ridge.
People in Murphy are nice and have a "live and let live" attitude. There has been and probably still is a problem with stray dogs (and cats) and not a lot of support for even something as common as The Humane Society.
I have fond memories of Murphy, but that's because I moved there needing peace and quiet. I knew it wasn't where I was going to stay and I feel there are a lot of more inviting places in the mountains.
As far as Robbinsville, I've only been there a few times. It is much smaller than Murphy and more isolated. I think the altitude is a bit higher.
I do recommend a visit to the wonderful Snowbird Lodge there if you get the chance. Other than that, it's just too isolated for me to ever consider.
Burnsville at least has somewhat closer proximity to Asheville and all that it offers. That alone would make it the number one choice for me.
Maybe someone can comment on Burnsville who actually knows something about it. I'm pretty sure the summers would be cooler than Murphy.
You won't get three feet of snow in a day in any of these places, unless it's a blizzard for the record books!