You Peach mainers probably don't know me, (as I do main Ness, however I have Peach as a secondary lol) but regardless, I'll give my 2 cents. =P
Anyways... Peach is definitely NOT an easy character to pick up. She has one of the highest learning curves in the game. As Dark Pch. said: "If you don't want to work that hard with this character, this is not the character for you."
She can rack up damage easily, though at times, it's difficult to land the finishing blow and people just want to force that kill, which is something you can't do as Peach. (I myself do it at times, which I need to stop doing)
Other common mistakes Peach players make are:
-Giving up too early
-Using Dair too much
-Abusing Peach Bomber
-Staling the hell out of her KO moves
And some others I can't think of atm.
She requires precision, great spacing, and having the ability to pressure your opponent and take advantage of them.
The main thing that makes Peach totally unique and different from others is her Float. Without it, Peach couldn't do every trick she can do. You need to learn how to use it well and wisely to be great with Peach. She has great qualities and it's definitely fun to win with Peach though.
In the end though, if you aren't that satisfied with Lucario, you probably won't be satisfied with Peach. And like Aleate said, you should be moving UP on the tier list from Lucario, rather than going down.