My ideals:
She can be a little more pragmatic as Supes while Kal can be a little more idealistic. These aren't extremes, Diana isn't bloodthirsty and Clark isn't mind-numbingly naïve.
Diana is more outwardly an outsider due to her lack of human guise. Clark was raised human so outwardly he can seem like he fits in just fine. There is a disconnect due to his powers, different physiology, and status, but basically he can hide it better.
Diana gives off a royal air. Not haughty but she is a princess, so that does reflect. Superman is far more laid back and easily approachable despite his powers. The royal air of the former makes her a little intimidating in terms of approaching her. However its not an intentional at arms length demeanor and she's actually quite welcoming and friendly too.