This is in other places, but I'll write it up right now because I want to play, but I can't at present... so I'll talk about it in lieu of that.
Big Band (6-4):
It is a guessing game. Guess wrong... ouch. Guess right... BB cries. I think PW has the advantage. You can stay comfortably at range until you are ready to move in. When you move in, BB has to play a guessing game. Unfly is useful in this match-up. Nails xx fly from full screen let you get in easy. If they parry, they lose A-Train charge. If they A-Train (most don't), your j.mp has a better than average chance of chewing through it. Also, if they are using a-train through it... unfly and punish. Watch out for giant step when you try and throw nails as you'll lose half your life if it hits. Beat Extend is always a threat, so be cautious of it. BB is always to be respected though because one successful SSJ can lose you the round. Play it slow, and play it smart.
Cerebella (4-6):
She has something for you at every range. Excellabella, DD, horns (to a much lesser extent) make our air-to-ground risky. Her air-to-airs beat ours clean. Her ground game is scary as fuck (throws for days), and her air-to-grounds aren't nothing to ignore. If you get in on a Bella, she fucked up. That said, it isn't nearly as bad as Parasoul.
Double (5-5):
I think this is an even match-up (and probably one of my favorites as soloWheel). Double can be hard to get in on, and she makes your nails a liability with truck special. Her j.hp is our j.mp only better. All that said, she still has to respect us, and we can put pressure on her that she has a hard time dealing with. In my experience, they are very prone to air throws same as us since they are often jumping around with j.hp.
Eliza:
She's not even out, so I'm not going to comment on her yet.
Filia(5-5):
I don't know... Part of me wanted to make this 4-6. If she touches you... you're likely dead. Her IAD bullshit can be tough as hell to deal with to boot. She does have a hard time making something happen though. Similarly, if you catch her, she doesn't have a lot to deal with us. There's a better than average chance she's mashing Gregor. Burst bait test her to find out. I find spending time in the air leaves her with only a few options.
Fukua(4-6):
She's rough to deal with. Pick a place on screen, and she's got an answer for you. She wins at range easy. She wants you at mid range which is where we want to be. Flying against her is rough as she's got answers for it. Armor isn't great vs her as she's got answers for it. Up close, she's faster than us, so you don't really want to be there either. On the plus side, if you hit her... she doesn't have a lot of answers. She is short on reversals. This is still a WIP since I don't get to fight competent Fukua's too often.
Ms. Fortune(6-4):
I was pretty convinced this was 5-5 for a long time, but I'd probably give it to PW these days. MF doesn't have a great answer for our air moves... and we're spending a lot of time in the air. She can be tough to get in on due to FU but she can't really capitalize on it too easily. It isn't an easy win, but advantage is ours.
Parasoul(3-7):
This will be controversial, but I think it is one of the few legitimate 3-7 MUs in the game. The rest of this is just a copy/paste from above... Her moves beat out ours in just about every situation. She can zone you. She has good defensive options in the form of Pillar. Generally, she beats you at every range, air or ground. To win you have to bait her into making a mistake, but she has the momentum starting the match, literally. Without an assist she is scary at the start of a match. Meaning you start at a disadvantage.
Peacock(5-5):
Another one I think could go 4-6, but to be equitable, let's stay at 5-5 for now. This matchup is super unfun win or lose. Peacock can zone like a boss... obviously. There's a real chance you'll lose half your health just trying to get a hit. Rushdown Peacock is not nothing though. High damage which leads to you sitting full screen eating a ton of chip damage... again... yay. But if you get in and lock her down, advantage tips to us. She does have a reversal and she's probably mashing it, so bait and punish it. She isn't easy to get in on though, and she's harder to punish due to bomb > tele shenanigans.
Squigly(4-6):
Squig usually has issues getting in, but due to our complete lack of decent ground-to-air, she gets to own the sky and start divekick bullshit which puts the pressure on us. Air-to-air her j.hp chews through fly and armor, so air approaches are hard. A few things help though. hk.buer from the ground will catch her j.hp. Charged 3.mp works well if she tries to dive kick. Thresher can catch j.hp for a huge punish, but it isn't easy to land... they have to be doing it predictably or you're going to lose meter for naught.
Valentine(5-5):
I'm going to say 5-5, but Valentine can feel like a better PW at times. Our mobility is more reliable. Val has to land eventually which gives us a window to exploit. But she's actually more reliable. She can turn any jump into either offense or defense, so be careful until you're certain she can't give you an airdash/double jump surprise. Patience is incredibly important as you're waiting for Val to overextend. She's also very fast. She can dash > airthrow from shocking distance, so never think you're safe vs Val.
@Dime_x
Why use PW/Beat Extend over say Val/Beat? The strong bit of that line-up seems to be beat (which I would argue is the single best all-purpose assist in the game), not PW... right?