Dear God this is a wall of text, I apologize in advance.
I don't know much about Peach so I may seem ignorant on some parts, so Dark.Pch can help correct my mistakes/rebuttle my points.
Options per Situation
Approach
Mario: Mario has Fireballs to help approach a grounded Peach, but Peach will never be grounded. Basically Mario has very little approach options in this match-up, anything else will get outranged by Peach, or we'll eat a d-air.
Peach: Peach has tons of tools to approach Mario. Floated aerials, Glide-Tossed Turnips, into what-ever she pleases. Peach will be approaching the most in the majority of the match-up, she'll try weaving in and out too bait the Mario.
Peach wins in approaching.
Defense
Mario: Mario has plenty of tools for being defensive versus Peach. SH, FH retreating Fireballs, up B OOS, FIHL -> Up Smash, up B, if Peach get's a little to anxious with her aerials.
Peach: N-air OOS (?), she has Turnips, Jabs, Grabs too try and keep Mario out of range.
Mario wins slightly in defensive options.
Edgeguard
Mario: Edgeguarding a Peach will not happen, period. Don't try anything too risky offstage with a Peach or you'll find yourself in a bad position. Best we can do is just use Fireballs to annoy her while she recovers, she'll take damage, but it won't stop her from coming back.
Peach: Edgeguarding Mario is tricky. He has a very high priority up B that will go through Turnips (?), he has a Cape to reflect the Turnips. However things get a little worse with Peach's f-air she will try and bait you into her f-air, or even n-air, once your hit you're not guaranteed to come back.
Peach wins.
Recovery
Mario: Mario has to best be very careful when recovering. FLUDD'ing her is probably a really good option since it pushes her back far if she tries f-air, n-air you. However she still has Turnips to try and make you waist our Cape.
Peach: Peach wins this for sure. She'll eat damage from Fireballs time to time, but she'll always make it back on stage, unless she makes a silly mistake and get's hit by a f-air spike, or get's knocked back to far from u-air or n-air. But still not likely to happen.
Peach wins.
Margin of Error
Mario: Mario doesn't have much room for error, he has trouble keeping the lead, and if we get too confident we will quickly lose that lead. Our defensive options just don't do enough damage to her.
Peach: Almost like Mario, if she makes too many mistakes she'll eat damage quickly. However she has enough options to bring it back, it's still risky though however, because of her light weight.
Peach wins.
Degree of Punishment
Mario: Mario can punish Peach if she is silly with her aerials, and she's predictable with her grounded moves she'll most likely eat a Fireball. Mario has tools to punish a Peach but as stated earlier if only his OOS did more damage...
Peach: Haha what can't she punish Mario has to throw? As long as she's careful with her aerials and avoids FIHL she will be fine. She has a many damaging ground moves (Uugh I don't like Glide Tossed Turnips >_>.)
Peach wins.
Character Attributes
Mario: Fast aerials, good OOS options, Fireballs, can live a lot longer, better KO options.
Strengths: Good range, good recovery, good options to punish, good edgeguard potential.
Weaknesses
Mario: Suspectable to being gimped if not careful, not good enough range, not enough damaging OOS options.
Peach: Poor KO options, if too anxious/predictable she'll take damage from Mario's OOS options, dies early, hard to score KO's.
Covering Weaknesses
Mario: can cover a lot of his weakness by just playing very patient, using Fireballs, FLUDDS, and OOS options carefully, and punishing Peach's mistakes when they happen.
Peach: Playing carefully, not getting too over aggresive, predicting Mario's defensive options and capitilizing on them.
Peach wins.
Kill Potential (Gimping would also go here)
Mario: Mario will KO earlier here. But landing the KO move will be very very difficult. We have dsmash that can KO, and it will most likely (and should) be unstaled, because she's always in the air. However fsmash will be most likely impossible to land, or very very difficult. Up smash can be landed if you catch her in a d-air and FLUDD it.
Peach: Peach will have trouble KO'ing, however she can rely on gimps, once you get Mario offstage at a very high % we'll most likely be KO'd from a f-air, or n-air. The problem is, is the % at which Mario will be at, and how much lower Peach has to be from being KO'd from a mistake.
Mario wins.
Damage Power and KO Power
Mario: Slowly but surely, pretty much sums it up for damage. Mario's Fireballs, u-smash, up B will rack up the damage (not much) but it won't be all that much. KO Power, Mario has stronger KO options for sure, especially against someone versus Peach.
Peach: Tons of damaging options, and plenty of moves she can do to keep her moves fresh, thus making it easier for her to rack up damage. Her KO Power if very poor, and this will help Mario be able to close the gap.
Even.
Gimp Ability
Mario: Very poor gimp ability.
Peach: Turnips, and punishing him when he makes a mistake, or mis-times a Cape.
Peach wins.
Overall
Peach wins this match-up.
Ratio
Disadvantage (40:60 - 35:65)