I only hunt here in Arizona and for elk it's drawing only, no over the counter permits. It can really be a while between being drawn. However the hunts are excellent. My last one was a couple of years ago, a 6x6 bull with a traditional muzzleloader.
This year I will be applying for archery bull and cow. I went too many years applying for the general (rifle/pistol) hunts where you chances are a lot less than the archery or muzzleloader hunts.
However I don't feel that there is any particular advantage or disadvantage between the muzzleloader or rifle hunts based upon the type of weapon. The archery hunts are a bit more difficult, but certainly not that difficult to get in close enough.
The Arizona regulations are out now and the applications must be entered before the closing date during the second week of June. Then usually around the 4th of July holiday the results are posted and the planning begins. The regulations are on the Arizona Game and Fish website at:
http://www.azgfd.com/ and you can apply on line there as well
The area, unit 6A, that I hunt in is between Camp Verde and Flagstaff and is Ponderosa pine forests and cedar/juniper range lands. Usually see pleanty of elk, often times very close and personal (like close enough to bounce a stone off their nose), unfortunatly that happens while accompanying someone with a tag when you were not drawn.