You can have two individuals, with similar musical technical ability, play the same exact notes on a guitar and receive completely different reaction from the audience. You can also have musicians who train day in and day out and become extremely good at technically manipulating their instrument but when you hear them play, they hardly evoke any emotional reaction in the audience. On the other hand, you have the other kind of musicians, who may either be technically good or not, but their delivery always triggers a palpable emotional reaction in their audience. So what is the element that makes the difference?
Well there are different aspects of musicianship. One musician might be great at 'arranging', another great at 'performing', another great at conceptualizing, orchestrating, etc.
For a musician to be great at performing, they must be able to evoke emotion, and react to the other musicians as they perform, and it requires a good ear for listening. The best improvisations always reflected the listening abilities of all the musicians. A good ear.
For a composer to be 'great', they should have the ability to create a 'freshness' along with accessibility. A great composer synthesizes his or her diverse influences into something new and exciting. The result should be music that is both unconventional and familiar while conforming to classical concepts of beauty- balance, contrasts, the opposites, etc.