I did not mind the KOA when we visited there several times, but LOVED Santa Fe Skies. KOA is more rustic. As you have a 36' coach, you could easily fit into most sites at the KOA. Both are about the same distance from the town but on opposite sides.
Whoops - just now read that you were going to Carlsbad. Also went there on our last trip (Sept 2013) We stayed at the Carslbad KOA. Level sites, clean. I don't believe that any nice RV parks that handle large rigs are close in to White City. There definitely is one just on the road after the turnoff to the caverns, but much better suited for tent camping or smaller RV - especially w/ no slides.
It will be about an hours drive from the Carlsbad KOA to the Cavern.