Actually, the meanings of "Prince" and "Princess" don't exactly correlate around gender.
The term "Prince" quite often means someone of power, a ruler. Me old mate Niccolo Machiavelli called his little book on the use and abuse of power "The Prince", and "Prince" in this case really meant "tyrant" rather than someone of undisputed royalty. Well, they were all tyrants in those days, weren't they? Nowadays we call them "president".
And Niccolo meant what he said, because he was tortured at least once by one of 'em, yet remained a fan of absolutist rule.
And "prince" can also be used in a genderless sense, too.
Queen Elizabeth I (Lizzy One) often referred to herself as a "prince" in the sense of "ruler".
"Princess", on the other hand, simply doesn't have the same connotations. Unless, of course, you refer to the current Princess Royal, who is recognised as something of a power in English royalty terms, but that's solely on the basis of who she is and her actions, not what her rank is. Sorry, girls!
