Tough choice! Both are pretty good episodes, honestly. Ultimately picked "Where No Man Has Gone Before" for managing to have just a bit more oomph in terms of stakes, but it really is a close thing for me.
Yes, both terrific episodes, right out of the gate. As fond as I am of WNMHGB, I voted for "The Corbomite Maneuver". The storyline is a bit stronger, in my opinion, and it is the episode that introduces "Bones" and Uhura as well.
Where no Man has Gone Before surely had the higher ambitions, but I like The Corbomite Maneuver better. It's more funny. And the Enterprise really feels like "home" in this episode. The characters are given so much attention. It is the expositoin of the series the pilot failed to be.
I voted for "the corbomite maneuver" (1x02), but actually I change my vote to "where no man has gone before" (1x01), since I think it's more interesting. However, I still like the first federation, fesarius, balok's puppet, and balok.