Because I think you've both done fantastically, and I can't find fault with either piece enough to differentiate, I think I'm going to point out a few small points in each piece, and then just say congratulations! I had to abstain from the voting, because I couldn't make up my mind. :D
Great job to be had all around. The characterisation was amazing, the descriptions powerful, and it was just all around great fun. I also really love to hate Aquila; I love how you've made a character so unlikeable, and you do a damn fucking good job of it.
However, there were still points where things may have flopped slightly. For one, I think that the fight scene was too short and abrupt. You limited it mostly to wordplay, and the actual battle was very short. Whilst Aquila is probably more of an intellectual than a straight up fighter, I felt a little cheated by the lack of straight up combat, partially for my next reason.
The next reason is that I feel like you missed the vibe of Walden and Kaiban. From what I read, though Walden seems strict, he and Kaiban seem too connected together to just betray each other by the flip of a coin. Though Kaiban might've been in shock, and Abra be a master manipulator, I feel like you really just completely glossed over the bond between master and student. It probably would've been more accurate to leave it as an inconclusive skirmish.
Finally, I want to criticise something else; Kaiban seems to jump too easily from emotion to emotion. He's not a 'green' gladiator who hasn't fought before, he's spent an extensive period of time fighting ghosts and spirits with various powers. He'd probably be hard enough to take adversity. You haven't really shown any reason for his emotive shifts, and that sort of lack of clarity breaks immersion. I know that 'show don't tell' is an important concept, but in this case, in regards to the transition, you did neither.
All three elements basically lead to the fact that Walden's death, which should've been incredibly emotive and powerful, was deeply unsatisfying. You left only a nonchalant acknowledgement of its consequences, and it felt more like one of those phoned-in TV serial deaths that they throw in for high drama without reason. It can be done right, but it wasn't in this scenario; it felt like I wasn't given enough of a reason to care.
Don't get me wrong, you still did a great job. Every other aspect of the story was amazing. Just a few things I feel like you might've messed up.
Well, since this is technically your first battle, welcome to the circuit! I hope you get the success you deserve. :)
I'd first like to compliment you on your general writing style. It flowed well, went along logically, and had a satisfying three-act structure. I feel like you gave us a very interesting battle, with the gunplay and cardplay mixing together well. Not to mention, the battle was long, enjoyable, and logical. It made sense how everything melded together. Even the suprise ending, having gone back through, made perfect sense; Walden's abilities and the firearm at close range would definitely have had that effect. As such, it was the perfect by-the-numbers battle. This made a little bit boring, but because the battle worked so well, I had no problems.
However, I do have a slight issue with the way you characterised Abra. The way I pictured Aquila's character was in a far more suave light, something along the lines of a more destructive Jigsaw coupled with Lucifer. I feel like you just compressed his entire character into 'insane.' This wasn't exactly a satisfying reading of his character, and it sort of niggled with me as I read along. I feel like reading the demo would've shown that Abra was far more slimy and charming than you've presented him.
That said, its probably more accurate than Aquila's portrayal of Kaiban, since you nailed Abra's lust for performance art as Aquila presented it.
Finally, the opening felt like you'd just sort of sped through something that should've been longer. Why are the two transporting Wildfire? Why didn't they just banish his spirit? Why did they need to take him with them? How did wildfire escape? The opening was too fast, and full of plotholes.
That said, you also did great. My opinion is really just being picky. :)
In summary, I can't give either of you my vote. I'll just abstain and drop my comments here.
I hope this helps!