A captain needs a loyal crew. The question here is: which captain has the most loyal crew? Its a very powerful and useful trait that assures the loyalty and the effectiveness of the people who serve under that leader. Both captains are well-represented in this category. Kirks crew were willing to risk their own safety to rescue him even after he was declared missing in action in the episode The Tholian Web. The same can be said of Picard when captured by the Borg in the episode The Best of Both Worlds. But, the difference between the two incidents is the way in which the crew reacts individually. To Picards crew, its a matter of professionalism. Options are discussed; plans are drafted and then, methodically, executed in a completely impersonal yet professional manner. To Kirks crew, its a personal matter. Spock, justifying his decision to stay and fight the Tholians as a logical one, is accused of being stubbornly loyal. In Amok Time, Spock also displays his unabashed devotion to this captain in an uncharacteristic show of emotional relief when he learns that he has not killed his captain. His yeoman wants him to look at her legs, his weapons officer constantly vies for his attention and the chief medical officer regards the captains health as his own personal challenge. Each member of the crew has some sort of personal link to Kirk, which is a stark contrast to Picards detached and aloof yet respectful relationship with his crew. Its pretty clear that Kirks crew has a deeper and more meaningful sense of loyalty to their captain.