Can someone compare them, between location, campus, academics, competitiveness, etc.?
UNCG is less competitive to get in. The percentage of students who are female is much higher: around 65% as compared with around 54% at Appalachian. UNCG is more racially diverse than Appalachian and there are a lot of gay students. UNCG is especially known for its music and theater programs, although Appalachian has a strong music program as well. Boone is, of course, smaller than Greensboro and much more of an “outdoorsy” place. Many Appalachian students are into hiking, skiing, and rock climbing. Appalachian has a housing crunch, which forces a lot of students off campus. There is a huge amount of school spirit, though, and most students who go there absolutely love it. Students usually stay on campus on the weekends, unlike at UNCG, where a lot go home. Boone gets very cold and windy in winter, something for any prospective student to consider.
Appalachian State is a better school academically than Greensboro. The average GPA and SAT for incoming freshmen is higher, the graduation rate is higher, etc. UNCG is a decent school in its own right, though. It all depends on what your criteria are.
Greensboro is a decent sized sprawling city with the campus downtown. You need a car, though, to really get around bc the downtown area consists of mostly businesses. Malls, shopping centers,most restaurants, etc are spread out all over the place. It is definitely not a city which thrives as a college town.
Boone is a small mountain town which is a college town. It definitely has a different atmosphere. If you love the outdoors, that would definitely be a draw.
App is more of a traditional college experience than Greensboro. Everyone who I know who goes there absolutely loves it. It is like a “hippie”, but I know plenty of more conservative people who have gone and liked it. Boone is a really cool little college town in the mountains.
UNCG on the other hand is a really quirky sort of school. I don’t know many people who have gone there out of choice, more so as a safety. From what I understand there isn’t really much of a campus.
The people who I know who have gone there and loved it were education majors. They have a great education department.
UNC Greensboro - Diverse, very good reputation. I’ve read the parking is terrible, but in general it seems like a good school.
Appalachian - A bit harder to get into than UNCG. It’s not diverse at all, it’s 87% white. Parking isn’t good here either. There is a bit of drinking/smoking, a problem at many schools. It’s a great school overall.
^ Appalachian isn’t a commuter school so parking isn’t important.
Essentially, Appalachian is in the top 5 public universities in North Carolina. Lots of school spirit, in the mountains, beautiful if you like the outdoors and skiing, more isolated, better if you plan to live on campus as most classmates will too. UNC G is one of the lower-tier public universities in NC, it’s urban and commuter, more diverse, better if you plan to just drive to school/take classes/go home and don’t care for the whole college experience.
I agree with most of the other posters. I’ve taught summer courses at App and absolutely loved it. ASU has a lovely campus in a great college town with lots of school spirit and some really nice facilities, especially if you’re in the honors program. The education program, natural sciences (particularly environmental), and music are particularly strong, but it’s at least decent at most things. App is in many ways a good blend of the western universities; it’s neither as isolated/outdoor-oriented/conservative as Western or as quirky/urban/liberal as UNCA.
If you’re interested in App, NC State might be a better fit than UNCG; the two share a lot of applicants. In the east, ECU and UNCW are also good.
UNCG tends to split applicants more with UNCC, which has been working hard to break out of its commuter school reputation/experience (new football team, new buildings everywhere on campus, etc.).
Much of Boone is very walkable (perhaps less so in the winter!), and App students can ride the bus (AppalCART) for free.
Oh please. When we’re not talking about the medical programs, ECU isn’t in UNCW’s league. 
App State is more equal to UNCW.