The only high level Peach who has played a high level Pokemon Trainer regularly is Edrees (vs Typh).
None of the rest of us know the matchup against a GOOD Pokemon Trainer.
At lower levels of play, Peach ***** fatties terribly, but at high levels, none of them perform that badly against her (Dedede, DK, Bowser, potentially charizard), so I'm taking Edrees' word for it.
Personally, I have more trouble with Squirtle...but I've never played a Typh- or Reflex-level PT, and Edrees has explained a lot of things about Squirtle to me that I didn't know.
Peach DESTROYS Ivysaur, so keep that in mind. He might be better to send out first just to get him out of the way. OR, arrange to send him in last and switch out as soon as he appears, giving Peach a free dair combo on you; probably worth it to not have to play a full stock as Ivysaur.