IC's only do really well against Link on FD. Other than that it's probably even or just a tiny bit in the ICs favor. Puff is about even with Link too unless the stage is gay.
Peach has an advantage against Link on small and really big stages, her shield pressure is incredible against Link and she can beat the nair all the time (which is Link's other shield). She's also hard to combo and, when she gets a turnip, hard to space against.
Peach isn't some sort of unwinnable matchup, I'd rather play against Peach than Doc or Mario, but she certainly isn't as good of a matchup as Link vs Jiggs, ICs or Samus.
Edit: Most people don't play enough ICs (or samus, or jiggs) to learn the matchup well. If you know the matchup it's not bad because none of those characters have a strategy that will always work. Peach is borderline because she has things that work retardedly well at close range and shuts down Link's major safety move. The only good thing about the matchup is that Peach is slow, which gives Link a good shot at spamming like a homo until he can land a kill move.