John and Joe, identical twins raised together, both complete the NEO, a personality test based on the Big Five theory of personality. How alike are they likely to be on the trait "openness to experience"?

No more alike than siblings.

Explanation:

Openness is one of the big five factors. it indicates that how much a person is open, extrovert. The person who score high n openness traits, he enjoyed life a lot and trying to keep in touch with new things. They always, imaginative and curious about their life. they enjoy their routine always. They usually imaginative and creative about life. They are enthusiastic personality.

In these traits, there are sub traits like:

imagination artistic interest emotional intellectual liberal extrovert

Openness is only a personality trait, that correlates with the neuropsychological test.