Cassandra Cain (Wulfmyth) vs Buffy Summers (KingGojira)

Cassandra Cain: The Batgirl, The BlackBat, The Orphan

Here's a quick bio:

Combat Skill:

So you started your post off by saying:

This debate is mostly going to be about Gear vs Stats, with a lot of debate possibly on skill. I say possibly as we may agree on skill, as skill wise I dont see either having a real edge. We can dabble in that later, but the core to consider is gear vs stats. Batgirl aha way more gear, but Buffy has way more superhuman stats and stated high level superhuman vs peak human Cassandra. 

I actually don't agree with this sentiment, nor do I think this is the narrative we should be taking in this fight. I believe skill is going to be a major deciding factor here. And, based on your post, Cain has a considerable advantage in this field. This is important because Cassandra's edge in skill has often allowed her to defeat people who are her physical superiors(something I'll go more in-depth about as the debate progresses). I'll break down the skill section like so:

1. Accolades

2. Training

3. Cassandra's special ability, and her major edge

4. Feats

Accolades

You've mentioned in your post how Buffy's skill is within the tier of Batman, Captain America, Wolverine, etc.:

Skill wise Buffy is really top tier martial artist. We are talking easily same levels as Batman, Wolverine, Daredevil, Cap America, ect levels. 

The funny thing is, all of the characters you've mentioned besides Logan, are inferior to Cassandra Cain, skill-wise. You have Batman admitting he'd lose to her(Detective Comics #951). After defeating Shiva, Oracle's files mark her as being "Unsurpassed" among the martial artists of DC's Earth(Oracle's files contain data on Deathstroke, Batman, Lady Shiva, Black Canary, among many others):

-- Batgirl: Secret Files and Origins

This is further backed up in the comic with the following statement:

-- Batgirl: Secret Files and Origins

And Barbara further confirms this by calling her technique perfect:

-- Batgirl #10

Already, just by accolades alone, there's a pretty clear picture that the former Batgirl is an incredibly formidable fighter.

But now let's move on to her upbringing and training.

Training

You've gone in detail about Buffy's innate talent due to her being a Slayer, and while you posted some impressive stuff, it's not better than anything Cassandra could've pulled off by the age of 9. She was trained since birth, day and night, by her father David Cain to be the perfect weapon with all of Cain's knowledge:

-- Bagirl #1

-- Batgirl #6

This is pretty noteworthy since David Cain is among the world's deadliest assassins(comparable to the likes of Slade and capable of going toe-to-toe with Batman).

While Cain didn't teach her every style of fighting, he taught her how to wield all lethal weapons, both conventional and exotic:

-- Batgirl: Secret Files and Origins

After losing her special ability for a brief period of time(don't worry, she regained it and I'll get into that later), Batgirl once again underwent training in all 127 major fighting styles by Batman:

-- Batgirl #7

It should be pretty obvious that Cassandra has at least basic knowledge on all 127 of these fighting styles as, even after regaining her ability, Cass still kept using Batman's holo-recording to train(it was not uncommon for her training to last days at a time).

We also know Giles train Buffy heavily in the art of blind fighting. Some examples here is her training with Giles, and fighting off 3 invisible demons trying to ambush her. 

Impressive, but pretty generic. Cassandra herself has stomped skilled assassins that could turn invisible like Camarouge, in Batman and the Outsiders. What leads me to conclude that Cassandra has better training is her tutelage under David Cain, Batman and Lady Shiva, who are the three most versatile and knowledgable fighters on DC Earth. This isn't even mentioning her training sessions with various members of the League of Assassins, Black Canary, Batwoman, etc.

But that isn't the really clincher for me. What is the real clincher is...

Cassandra's special ability

The Orphan has a special talent that she inherited from her mother, Lady Shiva. Due to her training with Cain, the talent was only boosted to the point that the language center in Cassandra's brain literally became capable of reading body movement and fighting as a form of language. This, in layman's terms, allows her to know what her opponent is going to do before he even does it:

-- Batgirl #1

-- Batgirl #4

-- Batgirl: Secret Files and Origins

Here's a bit more detailed explanation from Cassandra as to how the ability works, if you're interested.

Not even masters of hybrid fighting styles, like Batman or Deathstroke, are capable of fully countering this ability.

However, not only does this talent allow Batgirl the power to read opponent's moves, it also allows her to learn their fighting styles perfectly by watching and analyzing them. Batman says it took her five minutes to learn stick fighting(one of the rare things Cain didn't teach her because its non-lethal):

-- Batgirl #1

Cassandra herself notes that every fight she has teaches her something new:

-- Batgirl #64

And if you want to see it in practice, Batgirl learns the Koga-Ryu in seconds by fighting the Shadow Thief:

-- Batgirl #21

So in addition to allowing Cass to predict an opponent's moves before they make them, Cassandra can also analyze and learn their own fighting style and use it against them. I really don't think Buffy has what it takes to overcome this talent, but we'll see as the debate progresses. Now onto some...

Feats

I'm not gonna bore you and throw all my cards on the table just yet, so I'll list a feat I particularly like from Cassandra's Rebirth appearances. In Detective Comics #954-955, Cassandra massacres an army that contained 200 of the most deadly fighters in the world:

https://imgur.com/gallery/VBJjSUS

I haven't seen Buffy pull off a feat on this scale, but if you have something comparable feel free to show it. Now onto the big point I wanted to make with this entire section.

Skill Vs Stats

Now you've said that Buffy has superior stats, and due to my relatively limited knowledge, I can neither agree nor disagree. We'll discuss that as the debate goes on. However, even if I were to concede Buffy has better physicals, that won't be a problem for the Orphan.

Cassandra has straight up stomped metahumans with superhuman stats before, purely by using her skill:

https://imgur.com/gallery/4dFlY9V

This is pretty much in line with how her mother, Shiva, fights as well. Lady Shiva often uses her opponent's strength against them, as seen when she sent Supergirl(Matrix) packing:

-- Wonder Woman #175

So even assuming I agree with the idea that Buffy has better physicals, I've demonstrated Cassandra has superior skill and is no stranger to dropping metahumans. This, in addition to her capability to anticipate Buffy's movements, analyze her fighting style, and a gear advantage(I'll give details on Cass' gear in later posts), I think it's safe to say Cass has this in the bag.

Ball's in your court @King Gojira