When it comes down to it, there are a few things that matter more than others. How well a character does versus other meta relevant characters is the most important factor when rating a character (ie the MU spread). I would say that there should be some discounting for lower tiers: In practice, anyone below top 20-25 or so would matter a lot less than anyone in top 10 or top 15. I won't consider Lucina since she's basically Marth (and both Marth and Corrin go even with her anyway).
So then, who
is better, Corrin or Marth/Lucina? To answer this question, I will look at the MU charts of the three most notable Corrin players, as well as the three most notable Marth players. I'll start with
Marth.
MkLeo has Marth slightly
winning against Mario, Mega Man, Lucario, Peach, Toon Link, Villager, and Ryu (out of notable characters). He goes
even with Cloud, Fox, Luigi, Greninja, Pikachu, Olimar, Captain Falcon, and Corrin. He
loses to Meta Knight, Diddy Kong, ZSS, Donkey Kong, Sheik, Rosalina, Sonic, Bayonetta, and Mewtwo. Bowser is his worst MU (although MkLeo doesn't say whether it's 45:55 or 40:60, though I assume it's just an extra hard 45:55).
That's 7 winning MUs, 8 even MUs, and 10 losing MUs. The only top tiers he wins against are Mario and Ryu (if we consider them top tiers), while he loses to Diddy Kong, ZSS, Sheik, Rosalina, Sonic, Bayonetta, and Mewtwo.
Mr. E has Marth slightly
winning against Mario, Lucario, Peach, Toon Link, and Villager. He goes
even with Luigi, Greninja, Captain Falcon, Corrin, Mega Man, and Donkey Kong. He
loses to Meta Knight, Diddy Kong (significantly), ZSS, Sheik, Rosalina, Sonic, Bayonetta, Mewtwo, Bowser, Ryu, Pikachu, Olimar, Fox, and Cloud.
That's 5 winning MUs, 6 even MUs, and 14 losing MUs. The only top tiers he wins against is Mario, while he loses to Diddy Kong, ZSS, Sheik, Rosalina, Sonic, Bayonetta, Mewtwo, Cloud, Fox, and Ryu.
Pugwest has Marth slightly
winning against Mario, Lucario, Peach, Toon Link, Villager, Mega Man, Greninja, and Luigi. He goes
even with Olimar, Captain Falcon, Corrin, Ryu, Bayonetta, Bowser, and Sonic. He
loses to Meta Knight, Diddy Kong (-2), ZSS, Donkey Kong, Sheik, Rosalina, Mewtwo, Pikachu, Fox, and Cloud.
That's 8 winning MUs, 7 even MUs, and 10 losing MUs. The only top tier he wins against is Mario, while he loses to Diddy Kong, ZSS, Sheik, Rosalina, Mewtwo, Fox, and Cloud.
So that's Marth. That's an average of 6.66 winning MUs in top 25 (or so), and 11.33 losing MUs. He loses, on average, 9 MUs vs top tiers. That's... Not very promising.
Let's look at
Corrin now, shall we?
Cosmos chart is a bit interesting because he uses -0.5 and +0.5 for MUs that are often considered solidly losing or solidly winning. In order to reflect this, I will post them as is:
Corrin
wins 0.5 the following MUs: Rosalina, Luigi, Mario, Bowser, Peach, Villager, Lucario, Pikachu, Captain Falcon, Olimar, Toon Link, Donkey Kong.
Corrin goes
even with ZSS, Marth, Meta Knight, Mega Man, Sonic, Greninja, Ryu, Mewtwo.
Corrin
loses -0.5 to Cloud and Diddy Kong.
Corrin
loses -1 to Sheik, Fox, and Bayonetta.
That's 11 +0.5 MUs, 8 even MUs, 2 -0.5 MUs, and 3 -1 MUs.
Summary vs top tiers: Very slight (0.5) wins against Rosalina and Mario. Very slight (-0.5) losses to Cloud and Diddy Kong. Slight losses to Sheik, Fox, and Bayonetta.
First off, Ryuga has acknowledged that the Greninja placement is in error and is supposed to be +1.
Corrin
wins against Mega Man (+2), Toon Link, Pikachu, Lucario, Villager, Olimar. Corrin goes
even with Mario, Luigi, Peach, Rosalina, ZSS, Marth, Meta Knight, Sonic, Mewtwo, Donkey Kong, Bowser, Bayonetta, Captain Falcon, Fox, and Ryu. Corrin
loses to Sheik, Cloud, and Diddy Kong.
That's 6 winning MUs, 15 even MUs, and 3 losing MUs. While she doesn't win against any top tier, she only loses to three (Sheik, Cloud, and Diddy Kong), according to this MU chart.
According to Frozen, Corrin wins against Olimar (+2), Luigi, Peach, Bowser, Toon Link, Pikachu, Lucario, Villager, Mega Man. She goes even with Mario, Rosalina, Greninja, Sonic, Bayonetta, Donkey Kong, Marth, Ryu, Meta Knight, Mewtwo, Captain Falcon, and ZSS. She loses to Fox, Diddy Kong, Cloud, and Sheik (with Sheik being the hardest).
That's 9 winning MUs, 12 even MUs, and 4 losing MUs. No top tier wins (although Mario, Rosalina, Sonic, and Bayonetta are Even+), and four top tier losses (Fox, Diddy Kong, Cloud, and Sheik).
So that's Corrin. The average of Ryuga and Frozen's MU chart are: 7.5 winning MUs, 13.5 even MUs, and 3.5 losing MUs. Compare that with Marth's average of 6.66 winning MUs and 11.33 losing MUs and Corrin looks pretty good.
What if we include Cosmos' chart? Well, if we consider +/-0.5 MUs as even, then that changes Corrin's average to: 5 winning MUs, 16 even MUs, and 3.33 losing MUs. If we consider them as actually winning and losing, then that changes Corrin's average to: 8.66 winning MUs, 11.66 even MUs, and 4 losing MUs.
Some notes on Corrin: Some of the MUs can go either way. Many Cloud players, when asked, will say that the Corrin MU is even or slight disadvantage for Corrin, so it's possible that it's an even MU. There has been some talk about Diddy potentially being even as well. VoiD even put Corrin as "Even or slight favor" in his Sheik MU chart, although Corrin going even with Sheik seems a bit unlikely. Corrin has the potential to beat Mario, Rosalina, and/or Sonic in top tier, although all of these might be even (Sonic is probably the least likely).
Still though, Corrin losing 2-5 MUs, doing great overall against high tiers and high-mid tiers, and winning 0-3 MUs against top tiers is pretty solid.
Let's think about it. The two arguments against Corrin being placed high on the tier list seem to be the following: #1: She doesn't have results. #2: Her poor mobility brings her down.
#1 is blatantly false now. Now that Cosmos is able to travel Corrin is a pretty significant threat at majors. Even before we could see Corrin players such as Ryuga and Frozen take sets off top players. Cosmos, the best solo Corrin main, has better results now than Mr. E, the best solo Marth/Lucina main. Sure, there are more Marth/Lucina players than there are Corrin players, but since when has that been a good criterium for determining which character is better? With ZeRo gone, it's quite likely that Cosmos will end up getting better results than whoever the current best Diddy will turn out to be. The "Corrin has no results"-argument doesn't hold water anymore. I don't think it ever really did.
#2, well... Is this actually the case? I mean, she'd be top 5 easily if she had Cloud's mobility, but even with her current mobility she seems to do quite well in many MUs, slightly winning them or at least going even. Cosmos has pretty good results against some of Corrins worst MUs (Fox, Sheik, Diddy Kong, and Cloud). She's not Kirby, or Jigglypuff, or Ganondorf, and her tools work quite well despite her subpar mobility.
So, yes. I do believe that Corrin is a bit better than Marth.