Great read, makes me happy to see my main character remains tough in Brawl.
"Her double jump was DRASTICALLY reduced in height..."
Fair enough. Horizontal distance, plus ability to reverse direction, is sufficient. Although I fear I shall no longer be able to float above Giga Bowser's head...
"Peach is overall much faster than she is in Melee. "
An improvement. People often assumed Peach was a speed character (as most females are in fighting games), so they're doubtless catering to this stereotype. But I'm not one to refuse an improvement to my favorite character...
"Peach is one of the few characters that feels a lot like their Melee counterpart."
Good to hear.
"Peach's tilts all... setup nicely for an airial at the lower percents..."
Ah, yes! Her dreaded ariel attacks! Get 'em in the sky and send 'em to hell! Ooh-rah!
"Rather than being a wall of priority that can combo fast fallers this move is now a combo move on pretty much everyone. The move hits two times now, the first hit pushes them into the second hit, which sets them up for an easy combo."
I kinda liked the wall of priority, myself. But there appears to be a new combo emphasis for Peach. I approve.
"A lot of hearts and "pink" explode out of the point of impact when this move lands now."

They
had to add pink hearts. *Sigh.*
"Peach's down smash has been fixed. Well, I suppose the right word is nerfed, but you know what I mean."
Nooooooooooooooooooooooooooooooooooooo!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
"Peach's forward smash is a GREAT killing move in this game. It still varies between the frying pan, golf club, and tennis racket. The move comes out a little bit faster than it did in Melee and seems to have great killing potential regardless of which variation you get. This move is very strong and seems like it is hard to punish."
*Clang!* Ha ha ha. Finally, her foward smash will hurt like it sounds like it should.
"Peach's air game remained mostly the same. Still a lot of high priority moves, some with good combo ability, and some with good killing power. Her up air still does mostly the same thing, good for some comboing at lower percents, and can kill off the top at some of the higher percents too. Her down air is pretty much the same as well. Peach's neutral may have slightly less priority, but it's still great and does a lot of damage. Her forward air is noticably faster and still has good killing power. Peach's air game is really solid in Brawl, just like in Melee."
Godo to hear.