They're all pretty awesome characters once you crack open the surface and look deeper inside... (yeah, sorry...)
First off: Never underestimate Peach [https://www.youtube.com/watch?v=iwMvi8vzNhk]. In terms of characterization, since SMB3 Peach is the quintessential politician: she's always up to something but we're never quite sure what that is or how she's doing it. She is never simply idle, even whilst being held captive, and she is able to accomplish remarkable feats under the harshest of adversity, even more so than Mario. For example, in the aforementioned Super Mario Bros 3, Mario can't even find items like Jujem's Cloud and Power Wing, but Peach smuggles as many as 3 of them out of her captivity reliably after every stage.... via parcel post, of all things. Given Bowser's harsh security measures to keep Mario out, including several layers of military force and fortifications involving warping space... that can't have been an easy thing.
Zelda is a ninja, bard, fencer, and wizard all rolled into one. Her leadership shills are unquestioned, raised basically since birth to rule the complex politics of Hyrule's multiple races. She's a strong military leader, with command over countless armies - some of whom aren't completely useless - as well as a crew of pirates, and at least two entire ninja clans. Zelda also commands an alliance with powerful noncorporeal beings, such as the Great Fairies, the Guardian Spirits, and the Three Goddesses, whom she can call upon to aid her and her allies (specifically Link) with so little effort, she did it while unconscious. Several times. Similarly, following the events of their respective games, Zelda allies herself with former adversaries and rivals, such as Midna and Hilda (missing from the lists), and even Ganon at one point. Each of whom are at least her equal in all but popularity, and their friendship, however temporary, represents Zelda's general greatness.
Rosalina... isn't really a princess, she is Queen of the Stars; Mother of All Lumas. Still counts though, I suppose. She is by far one of the most powerful of Nintendo's "princesses", with direct control over time and space (fueled by Power/Grand Stars), and the magical ability to conjure Lumas into being, who then become new stars and planets when fed (some of whom may contain Power Stars of their own). Honestly, one wonders why Rosalina needs Mario at all... (Truth be told, she doesn't. She's helping Mario because he asked for aid and she responded.) Rosalina is similar in power and ability to Nintendo's other godlike "princess", Palutena from Kid Icarus - who is strangely absent from the list of choices.
Daisy is an interesting character in her own right, though her development has been severely limited by her lack of exposure. Daisy is the ruling princess of Saharasala Land, the setting of Super Mario Land (which coincidentally shares a name with one of the Zelda series' mentor Sages), and somewhere we've never been to since. There have been places with that name, and Daisy does come by to visit and play Tennis and/or board games from time to time, but no other characters from that game have ever returned. Daisy is described as an athletic tomboy and brazen, outspoken counterpart to demure Peach. Other than that, she hasn't really done much "on camera". Until she gets a more prominent role, she's "just another princess", similar to Mario's first girlfriend, Pauline - whom we hadn't seen since the original Donkey Kong (until the recent Mario vs Donkey Kong, where it seems she became a television celebrity of sorts, but little else is explored).
A few other Nintendo "princesses" of note:
Tiny Kong, a direct relative of Donkey and Kranky Kong, and therefore holds some claim to their fabulous "wealth" (of bananas) and lands (though she is owned by Rare, so... maybe not "technically" Nintendo-brand).
Krystal, the psychic fox princess and ruler of dinosaurs who also happens to be a skilled Arwing pilot.
Lucina... she's from Fire Emblem, everything else about her is a spoiler if you haven't played it yet, but trust me, she's badass.
Jenna, the flame-wielding, rock-blasting, spirit-taming, dragon-slaying badass from Golden Sun also happens to be the daughter of a chief elder of their Adept village (so technically a princess).
