Unit 13 is a desert unit and much of it holds very few elk. Also, there are large areas of private ranches throughout the unit, and the Puebla of Acoma in the northern part. That said, there is plenty of public land. I've only hunted unit 13 once, in 2002, but killed my biggest bull to date, an old bull that weighed right at 1,000 pounds and had antlers scoring 386. Due to extreme drought, he lacked top end length, but had great mass throughout. I would suggest you look at public land east of Pie Town and north of the Southern Cross Ranch. Your tag is early and it'll be hot, so hunting water will be key to success.
Unit 10, I hunted Pronghorns there last year. There are some big bulls to be found there but I don't personally care for 10 as an elk unit. You'll be amazed at where you may find elk. I found a group of bulls in the northern end of the unit, right out by Cataract Canyon. They were bedded in the sage, miles from the nearest tree. If I had a unit 10 elk tag, I'd be sure to purchase a Boquillas Ranch permit and hunt near the boundary of the Hualapai reservation.