I've got a thing for Mule Deer. That being said Elk in the rut are a close second! If Washington had more favorable elk hunting it would be closer for me.
No debate. Mule deer! With that said, elk can be useful - I once slipped in on a nice mulie buck who was preoccupied with a bugling herd bull and the commotion of his cows.
I've never hunted muleys, but I would really like to try it out. I'm more focused on killing my elk first, then muleys after, maybe because I've hunted whitetails so long that muleys don't do it for me yet.... I did stalk up onto a nice 5x5 muley while elk hunting in Idaho last year. Besides, I like game that I can call in to me (ducks/geese #1 followed by elk and then turkeys!)
I do my best to love them the same. I have to pick one or the other when i am hunting though, especially with the bow. Otherwise I won't do either well.
Elk bugling in full rut only reminds of one thing, that I've missed my opportunity to kill that big muley while he was still in his velvet clad summer mode!!!
I must admit, elk hunting is fun but nothing like hunting mature mule deer. Biggest problem is that few places have the number and age necessary to produce real mule deer.
I grew up hunting mulies and so they're my favorite. But bull elk are a close second. Both can get the heart rate pumping. But I'm mostly looking to put meat in the freezer. If I can hang it on the wall that's just an added bonus