I've always field dressed my animals even when I am planning on boning them out, but then I also bring the heart and liver home and you don't have to worry about making a slip when you are cutting the rib meat out.  If you do do the gutless method you can still reach up into the body cavity and cut out the tender loins but just not as easy. 

I have always gutted all my animals, as I have always had to quater them to get them ouf of the hills.  I have always wanted tor try the gutless method way also though.  Seems like it would be quicker and cleaner at the same time.  As far as the tenderloins go you go behind the rib cage and in front of the hinf leg up near the spinal cord.  From what I have read it takes some time and you have to be real careful as you are going in blind and will not be able to see where you are cutting and the last thing you want to do is cut yourself in the back country.  I am gonna try it on an antelope this year and see if I can practice a bit on a smaller animal. 

Here is a link to some videos on how it is done.

http://elk101.com/webisodes/gutless-video/

I've used the gutless method on the last two elk and I think it works great!    You can open up a couple ribs and get in for the tenderloins.    

I didn't like it, it felt awkward to me.  And when taking meat off the bones, you still had to be extremely careful around the body cavity.  This includes cutting meat near the pelvis, the backstraps, and any rib meat you might want.  For the last several years, I've been carrying a few pairs of nitrile gloves with me, and found those to work just fine while gutting.  This way I don't get blood in my fingernails that stays there for two weeks.  I also feel like you will cool the meat down faster if you gut the animal, but that's just a hunch.

I use the gutless method, and lately i've been deboning too. Deboning without gutting is tricky, but still better than hauling out the bones. Elk bones are heavy.

For deer I just use gutless, and don't debone.

When it comes to elk I prefer to gut them first just simply because it makes them easier to move. I have even used the gutless method on the 3rd bear I took. My brothers wife shot an elk 3 or 4 years ago and happened to gut shoot it. I definately used the gutless method on that one.

Quinton

As previously mentioned, saw a couple of ribs carefully and you can access the tenders.

I like to gut them because they are easier to move and here where i live they like to do testing on the different orgins. 

I do both and much of it depends on how the animal lays,terrain how far I have to go to get to horses or truck. I dont however agree with gutless fanatics that its any easier or faster as we have timed both. I think alot of folks jump on it just because its the new next best thing even though guides and outfitters been doing it for years now.