I suppose, but you do not have to be completely equal to clash out and have both attacks blow up.
If you want to match the other person's technique, then yes, you need to match it.
-Chidori vs. Rasengan. Naruto and Saske clash, and they tie every single time, but at the hospital, Naruto was heavily implied to be stronger, and it was said that Sasuke could have died had they clashed, meaning Naruto would have won and Sasuke would have lost, because his jutsu is weaker. PS Chidori vs. Bijuu Dama is an obvious parallel of Naruto and Sasuke's final attack at VoTE back in Part 1. They are equal.
Sasuke would have to get close up to Madara, in which case a direct sword slash would be able to counter a Chidori.
Sword slash is weaker, and Chidori has enough power to damage PS's body let alone it's sword. Sasuke rips through Madara's sword and stabs his Susanoo with Chidori. Repeats the process till he breaks through and then Madara dies. Not to mention Sasuke's Susanoo can teleport due to Amenotejikara, so he can hit Madara with back attacks, meaning he won't be able to block or retaliate.
He can also simply push his wrist up and attack with the other hand. It could go many ways, but Sasuke isn't simply going in unharmed just slashing with Chidori
Actually he will. If Madara tries to do anything, he gets hit. Push his wrist up? He'd have to be able to outmaneuver Susanoo to do that, and that is something he can't do, not when they are using the same exact level of Susanoo. He'd also have to be able to react, which he can't do since PS can teleport via Sasuke.
It didn't drastically increase. We never saw EMS Sasuke's Perfect Susano'o to compare, nor do we even has solid evidence that he had one. That means you'd be comparing Sasuke's legged Susano'o to Madara's Perfect Susano'o, which are from from equal.
Irrelevant. I don't need to see it to know that it was weaker than Madara's, or equal at the very most, and Madara only cuts Mountains. Sasuke's Rikudo PS cuts CT that dwarf Mountains.
Also, where is the evidence that it didn't drastically increase? Cause all manga evidence shows that it did.
The tailed beasts couldn't even get up in time and got chained. It's not like a punch is going to rip limbs off of them. Even if they somehow, for some reason, weren't able to crack Susano'o(though Raikage was able to), they are definitely knocking it back some ways. The Perfect Susano'o is nowhere as dense as a tailed beast.
Couldn't get up, got chained=/=Took heavy damage.
Not only is density not the issue here, PS is far larger than Hachibi, which took Limbo with no damage. Hachibi gets wrecked by Bijuu Dama. PS tanks a Bijuu Dama far stronger than that with minimal damage.
It's simple logic. Sasuke had his Susano'o use Chidori. It obviously became larger and stronger. If you have the Perfect Susano'o use the jestures for a Rinnegan technique, then it would come from them, therefore a larger magnitude.
Chidori got stronger because it got much larger.
-Asura Path isn't usable with Susanoo. It summons weapons onto the user's body, pretty sure you can't do that with Susanoo, and even if you can, you have zero feats to believe it'd be strong enough to do anything.
-Animal Path is irrelevant.
-Human Path is irrelevant.
-Deva Path's jutsu don't increase in size with the user, so it'd be the same whether PS used it or not.
-Narak Path is irrelevant.
Sasuke using Chidori w/ Susanoo=/=Saske or Madara using any technique they want with Susanoo. Get feats or logical reasoning behind it or don't argue the point.