It certainly depends on which cookie and which brownie we are talking about; generally speaking I like cookies better. My favorite cookies are the butter cookies filled with dulce de leche, a personal “alfajor” style treat, which I describe in one of my dessert Hubs
This is a very tough question as I am fond of both. As per your question, I go for tasty brownies with chopped nuts and straight from the oven, well-baked and tasty and served with a dollop of vanilla ice cream and drizzle of chocolate sauce!
Tough decision but I think cookies because there are so many great varieties. I like really chewy cookies with white chocolate chips. Brownies are a very close second, though. Boy, that's the hardest question I've been asked all day