Based on your question of Nevada or Arizona, but not both, I'd go with Nevada. As RamDreamer said, you get to apply for three species of sheep. But, there are a few other things to consider that tip the choice toward the Silver State. First, Nevada has a lot more quality mule deer hunting than Arizona, and you can draw about every five years, way more often depending on what hunt choices you apply for. Arizona, if you're hoping to draw a strip or Kaibab late hunt, is a one time deal for a non-res, and only those with max points have a chance at those tags. You do have a chance at early season tags, whitetail tags and lesser mule deer units, but not late tags north of the Grand Canyon, unless you have maximum points. As for elk, both states have excellent elk hunting with terrible odds. You'd be lucky to draw an elk tag before 5 years in either state for most of the choices, a lot longer if you're putting in for the top hunts. I've had the good fortune to go on five elk hunts in Arizona over the last twelve years, but only two of those were on my own tag, while three were with buddies in lesser regarded units.
Now, to sheep. You have a statistical chance to draw either state with no bonus points, but whether you're at zero or a dozen or more points, the odds suck big time. I don't think DonV quite understands Nevada's system, as you can actually draw with no to very few points, though it's very unlikely. Nevada squares your points each year, and the more points you have, the better chance you have to draw a low random computer number. Each applicant only gets one chance in the drawing, and the advantage of someone with ten points is that they'll get 101 chances to draw a low number, whereas the applicant with no points gets one chance at his computer number, the guy with 1 points get 2 chances, 2 points gets five chances and so on. Once random numbers are assigned, everyone goes into the system ONCE, WITH ONE RANDOM NUMBER ONLY. This applies to all species, not just sheep, but I wanted to answer your question about sheep specifically. In Nevada, once you purchase your license, you can apply for each species for a cost of $10-$20, approximately. I apply for my twenty year old son and I, and we apply for all species for both of us. We put in as individuals, that way if either of us draws, we get to go hunting.
With regard to Arizona sheep, there was a misinformed quote above regarding there being no chance for anyone other than a max points holder to draw a sheep tag among the non-resident allocation. Arizona doesn't use the "max pointholders pool" when drawing sheep tags, like they do for deer and elk. With sheep, they're just like Nevada in that everyone's name goes into the computer once, it's just that the guys with more points get more chances for a low random number.
One other difference that might matter to know if that Nevada has a dedicated allocation of tags for non-residents, whereas Arizona allots "up to" 10% of their tags, but none are guarantted to non-residents.
If you really want to hunt sheep, you might consider doing what so many of the rest of us do, which is to consistently apply everywhere you can. Each year, I apply for my son and I both, in California, Oregeon, Nevada, Arizona, New Mexico, Utah, Colorado, Wyoming and Montana. I don't apply in Washington or Idaho, even though Idaho has perhaps the best sheep odds of any state.
I hope this helps you.
