Zelda is more than just a Princess. She is the leader of the Sages and she possesses a piece of the triforce. She possesses her own unique abilities such as the ability to fire light arrows. She often fills the role of side kick to Link and in several games it is impossible to beat the final level without her assistance. Zelda knows how to ride a horse, fight with a sword, shoot an arrow, fight hand to hand, and has her own magic abilities. She is wise and elegant and graceful. She will help Link in battle either with advice or with a sword in her hand. She will cross unfamiliar landscapes and battle monsters to aide Link. She has traveled through time and in Wind Waker was even a pirate!
Zelda is an example of a well written strong willed female character. The difference between her and Peach is that Zelda often goes to great lengths to avoid capture from the enemy, can survive on her own, and will attempt to escape from the enemy herself. After she is freed she will join Link in battle and combine her powers with him to seal the enemy away and win the game. Zelda is not a weak character because like Peach she is often captured and fills the role of Damsel in Distress. Zelda is a good character because unlike Peach she does not always need a male to rescue her. Zelda is fine 90% of the time. In Skyward Sword it is only in the last half of the game that she needs rescuing. For 90% of the game she is running around having her own adventure and avoiding Link.
It isn't necessarily bad for a female character to fill the role of Damsel in Distress. I don't think it reflects badly on Zelda's character that there is a point in every game when she needs Link's assistance. It's okay to ask for help. What's annoying about Peach is that she never tries to escape herself or to avoid being kidnapped again. She just screams "Marrrrioooo!" and waves a tissue. At least Zelda makes it difficult for the baddie to capture her.