We're pretty close on this, so the following is not really an attempt to change what I think is a pretty reasonable position. I'm really just mentioning it because I thought of it after my last post.
We've both used anecdotes where the style of one captain seems less able then the other to succeed. But I can think of one situation where Kirk and Picard faced substantially the same problem, and I think it's pretty telling.
In "A Taste of Armaggedon" and "Symbiosis," Kirk and Picard, respectively, wrestle with obeying the Prime Directive yet allowing great suffering, or violating the PD and alleviating the suffering. Predictably, Kirk violates the Prime Directive, while Picard does not.
Picard could actually have alleviated the suffering of an entire planet when he discovered that a required substance from one planet was not actually a treatment for all the inhabitants of another, but a non-fatally addictive drug fraudulently PEDDLED as a treatment-- for generations. All Picard had to do was say something. Picard chose an extremely narrow interpretation of the PD that didn't even allow him or his crew to intimate that a devastating lie was being perpetuated. The Prime Directive was followed, but an entire planet not only suffered, but in fact continued to toil relentlessly for the society perpetrating the fraud.
Kirk, on the other hand, was faced with two planets locked in perpetual war. They were able to have this war last indefinitely because they had negotiated a mutual agreement to wage war cleanly via a number of treaty-specified computers. The end result was that bombings occurred virtually, sparing crops and infrastructure and allowing the society to survive. The drawback was that people labeled as "war dead" in these virtual attacks were required to report to incineration chambers. Typical for Kirk, an extremely attractive and suspiciously underclad young hottie was involved. Kirk thought very briefly about the situation, pulled out both phasers and started blasting the incinerators. He destroyed the war computers on the gamble that when faced with the prospect of a REAL war, both sides would choose to wage peace.
The end results-- Picard allows an entire planet to wallow in suffering and virtual slavery but keeps his precious moral purity intact, whereas Kirk blows stuff up, stops the perpetual war, AND gets the space chick.
No contest.
--alt- "I have a good suggestion for who here should be Neelix-- he's affable but not good with numbers" -eran