Peach is definitely the #1 Video Game Princess: She's strong, playful, and loving and everything, not to mention she's the Princess of the #1 Gaming Franchise: Mario. She's got it all for the #1 Spot. Zelda is good and all too, but unlike Peach, Zelda isn't the Princess of the #1 Gaming Franchise.
You should see the Princess Peach in Super Paper Mario, she's got Near-Invincibility with her Parasol, and her Strength is right up there with Mario and his Brother, not to mention after you level up so high and power up with countless HP and Power Pluses, she can kill almost everyone in one hit.
As for Brawl, she's a powerful killing weapon, only successfully equalled by very few: Captain Falcon, Diddy Kong, Snake, Toon Link, and Wolf. And only successively surpassed by Marth. She even surpassed Mario! She has a unique Projectile Attack and the ability to float, which really makes her absolutely deadly in combat; you can use her Standard Air Attacks, advance on opponents from above, or combo opponents after you've knocked them into the air with a Throw or Smash Attack, just to name a few. This also aids in horizontal recovery.