I do agree that a good leader should follow logic on most occasion. But Kirk was logical man. Of course, it did not come to him as natural as to Spock, but many times, Kirk managed to solve logical problems which nobody else was able to solve (The Ultimate Computer, I, mudd ...). But there are also another features a good leader must have and intuition is one of them. Spock denied his intuition with the rest of his human part so he was unable to have those "hunches" his captain had. Logic is a good friend, but if there is not enough information, it is totally useless. In such situations, Spock was usually unable to do something, but Kirk was (The Corbomite Maneuver, The Taste of Armageddon). Moreover, Kirk was also a better leader, since he was a human so he could identify with the rest of the crew, who liked him because of that much more. I like Spock - in fact, I am very similar to Spock - but as a leader, I would still prefer Kirk.
Kirk has a bigger ****?