A Hime-sama is rich and beautiful like a Ojou-sama, but personality wise is very different.
They're known for their kind and elegant personalities, generally soft spoken, and as opposed to a Ojou-sama's boredom with mundane life of common folks, Hime-samas might marvel at it.
They wouldn't be the bossy sort in the relationship, and if anything are prone to being naive and innocent when it comes to such things.
Hime generally means princess/ young lady of noble birth; similar to Oujo-sama and Ojou-sama, but could be used to be different.
Examples
Tsumugi (K-ON!)
Tomoyo (Sakura Cardcaptor)