I have extensive experience with both and what I can tell you is this:
I enjoyed running the Nitto Trail Grapplers and found that they worked well on the trail. They hooked up well on the rocks and seemed to wear fairly well. What I didn't like about them is that the 37's only came in a Load Range C and their sidewalls weren't as strong as I would prefer. I also didn't like that they weren't offered in a 13.50 width. On pavement, they were pretty quite for an MT but they had a strong radial pull to the left and I found that to be annoying. Overall, they're a good tire, their 37's are made in the USA and I would run them again if I had to.
Cooper Discoverer STT Pros are what I'm running now and I absolutely LOVE them! They hook up MUCH BETTER on the rocks and so far, I've found them to wear much better than the Trail Grapplers. I LOVE the fact that they're 37's are available in a 13.50 width and in a Load Range E. The sidewalls on their 37's are extremely tough and I haven't noticed any radial pull from them. They are a bit louder on pavement but just by a bit. If it matters, they are without question, the BEST MT I have ever driven on in ice and snow. The other thing I really like about them is that I could get 5 tires for the price of 4 Trail Grapplers which is quite a deal and of course, Cooper are made in the USA.
Hope that helps.