Well i guess i'll start.
Close Range:
It might just be because i play heavily grounded. But a good Peach player can easily float around links head height and can easily avoid all of Link's ground based attacks. Float just out of range, and wait till he attacks. If he tries ground based attacks, Dair Nair and Fair can all be used to punish him. If he chooses to jump for an aerial, Nair or Dair would probably beat him there. There isnt much Link can do in this position but attempt to get away.
A ground canceled aerial into jabs just own Link. As there is nothing he can do in this scenario either. Except defend and run away.
Overall Link gets owned by peach in close range.
Mid-Long Range :
Link's projectiles spam will probably win him a long range battle. 2 bombs, arrows, boomerang, and zair can make it really hectic to try and defend against all of them. Im also pretty sure bomb at least clank with turnips if not beat them. Same could be said about the other 3.
Aerial:
Peaches air mobility and high priority aerials most likely allow peach to own the skies. Only thing to watch out for are projectiles, Zair, and perhaps Dair. Everything else can probably be out prioritized. Fair might be able to out range peaches aerials. But due to her air mobility, peach can easily back up and attack after Fair is over. Also be aware of Uair's vertical range, but it has very short horizontal range.
Link Offstage:
Total cake walk for Peach. float off backwards with Bair will probably kill him and probably Fair. A dropped turnip will most likely kill him as well. Note that some Link's will attempt to recover high against peaches to avoid being gimped.
Peach Offstage:
Not much Link do against peach without risking his life. He could projectile spam to keep you back. Though Bombs would knock you high enough to recover no problem. Boomerang may end up pulling you back to stage. Arrow may be the only truly useful thing in terms of gimping. An uncharged arrow is enough to stop peaches float and a charged arrow will stop peaches momentum as well. Watch out for Nair, Fair, and Bair when you get close to the stage. Also be aware of the 3 zair invincible edge hog. Probably peaches biggest worry will be about Link's Dair. Its slow moving and long lasting, making it hard to air dodge. It seems like it would always be best to attempt to recover high by using float to avoid most of Links efforts. Just watch out for Uthrown bombs.
Kill Potential:
Link clearly has more killing potential against peach in both power and weight. Dsmah, Fsmash, and Dair are Link's most powerful killing moves. Though if Peaches floats in the perfect spot she can avoid both Dsmash and Fsmash for all of the match. Link will probably be forced to use a lot of Utilts against Peach, which will stale that move and ruin its kill potential.
Peach on the other hand has air mobility and a good horizontal knock back move that could kill Link fairly early and of course turnip gimps. While most Peaches ive played spam the crap out of Fair, i think it would be best to save it as much as possible to keep it fresh. It Peaches best killing option against Link.
Overall:
Peach has the advantage if she plays smart.
Anyway i hope that helps a bit.
. The night is still young~
