As you can see, the Cocoa Brownies with Browned Butter are much darker and shinier than their simply Brownie plate-mate. They have much more cocoa, a bit more butter and the same amount of eggs and sugar (+/- 1/4 c), and they are much(!) richer, fudgier and decadent. Nanny's brownies, by comparison, don't feel as sinful and tooth-achingly sweet (I don't mean that in the pejorative here) but they just aren't as good so I'll go with the wow-that's-a-lump-of-chocolate-brick in your stomach feeling in the future.
Regarding the nuts, they lend very different tastes but I don't have a preference. I love the pecaniness of the pecans but I also love the more austere, buttoned-up'ness of the walnuts.
Bottom line: go with the Cocoa Brownie with Browned Butter recipe but try it with both walnuts and pecans to see which you like best. And whatever you do, don't eat these without a nice glass of cold milk in near reach!