So far I am the lone Mule Deer voter.
Let me tell you why I would suggest Mule Deer over the elk tag. Simply put there are a few more deer around and they are a bit easier to hunt. IMHO elk are a step up from deer and in my own personal progression chart I always take hunters new to hunting the west on mule deer hunts first then after that on some elk hunts.
I just feel it's a bit easier to find and take deer than elk. Elk generally require that you get further back in and require more patience and skill to take.
I am not suggesting in any way that you aren't skilled, just that if you haven't yet taken either I would suggest crossing the mule deer off the list prior to chasing the elk just for the experience factor.
Just my 2 cents.