I think when a person has power, the main challenge is to keep it in perspective. Those who are uneducated will misuse or abuse power. In fact, the educated person will know that power isn't really power, but more along the lines of "influence", because really, not one person can have all the power - it must be diseminated properly through the right people.
When someone says another is "arrogant", it brings up all the flags of a person who has low self-esteem to the person doing the labelling. Perhaps one believes in themselves so much that they must say it. Really, it's all about perspective.
I can think highly of myself without such a trait as arrogance, though those without such confidence may see it as arrogance.
To answer your last questions, I think it has everything to do with how the person or organization conducts itself when they know they have the power but does not flaunt it. Winston Churchill was considered powerful by many, knew how to control it, without humility at times.
Commenting by HaloScan
