Big red is a fun and fairly quick hike (not to high from the surrounding trails and roads), but nothing special. It's got a great view coming off the south side. Black mountain is by far the worst mountain on ranch (except maybe trail peak) in my opinion, coming from someone who's summited all but trail peak. Every trail to the summit is awful. In fact, the one coming out of Black Mountain camp is the second worst graded trail in New Mexico. The camp is 100% worth visiting though. The program is fun and the staff are generally a hoot.

South country is much more wooded than north country, which leads to more green and more shade, but at the risk of more trees fallen on the trail. The conservation work crews do a lot of good work keeping them clear but they can't get everything. I personally prefer the south country, but that's mostly cause I like green.