You haven't met my wavedsashing Peach. She actually has a tiny speed advantage when you compare her WD to Ganon's, and as for distance, it's somewhat irrelevant as a well executed WD is enough to bring Peach just out of range of any of Ganon's attacks. It's not like Ganon's is much better, and his SH WDs don't really hold much to prevent turnips from hitting you. >_> Also, her attack speed is quite a grade higher than Ganondorf's.
As for turnips... catching them is more or less what Peach wants Ganon to do, because it severely limits his options (everyone's actually, except fellow Peaches). Even if Peach gets hit by the turnip, it's just a turnip, not f-air or d-air. Given that turnips are also so easy to see coming, throwing them right back at her is simply Toad bait. Alternatively, she can float and use nair or bair, because those are both strong enough to bat away any turnip save death, and have large enough hit windows to hit Ganon in the same attack if he's close. The people I face generally prefer attack right through the turnips instead of catching them.
As for priority, please... it's Ganon. He both overpowers and outranges Peach by a long shot. If you're exceptionally good at spacing yourself and your ranged attacks, Peach will have a tough time laying on a good offense without the aid of turnips. Factor in the turnips and Peach sneaky approaches though, and the gap in priority quickly closes.
Staying power is also pretty obvious. Ganondorf is much heavier and harder to KO compared to Peach, and has a lot more KO power compared to Peach. Peach's advantages here are her edge guarding abilities against Ganon, Ganon's lack of edge guarding ability vs. Peach, and Peach's recovery in general.
The mind games... Peach probably has the most diverse shield game in SSBM. WD, SH aerials, turnip throws, dodges, shield-JC, etc. are all bound to leave you guessing as to what she'll do when you try to attack her. Direct encounters themselves can be lacking because of the onslaught of turnips and Peach's ability to run away from a guy like Ganon.
>As for Peach's offensive mindgames, they are more varied than Ganon's can ever hope to be. The turnips, slap setups, float variations, the general keep-away game, and fear of dsmash will limit Ganon's "safe" options. Dire and I will be taped to the best of our ability.