arundodonax wrote:So if you were just exiting from one, which one would you pick - New Army or Cottonwood?
As each of the experienced hikers have mentioned above, it's all a function of where you're going and/or where you've been.
If you stay in the Cottonwoods basin, then there really isn't any need to go over any of the passes (CW, NAP, AP). For those who like to fish, specifically, for anyone who likes to fish for Golden trout, the CW lakes region is a home run.
However, if you want to check out Miter basin, then you're talking about going up & over the Sierra crest. If it's only a day trip from a CW base camp, or a 1 night stay over, to either fish Sky Blue, Primrose, etc or climb Langley, then the preferred loop is over New Army<-->Army passes. (When the snow clears - see my account of AP from a few weeks ago.)
OTOH, if you are thru hiking from/to points north such as Whitney, Kearsarge, Big Pine, etc, then some prefer to cut the distance & height (climb/descent) by going over Cottonwood pass. Not to offend anyone, but CW pass is a lot like LA: it's just a place to try and get through as quickly as possible. (And I can say this because I live down here.)