Alright, sorry I've been unable to really respond for a week. I'm actually gonna go in-depth.
First things first, AP. Superman currently scales to around 1.08 KiloFoe, whilst Batman hangs around the 2.7 KiloFoe range. Giving Batman a solid 2.5x AP advantage.
Abilities would go to the Man of Steel, he's able to mix and mash with Heat Vision, Freeze Breath, intangibility and invisibility, Illusion creation if the fight gets heated, Regeneration to repair any bad wounds. Though Batman does have a decent amount of counters, attack absorption/redirection, Nanotechnology which could act similar to regen.
Skill would obviously go to Batman, though this version of Superman is no chump when it comes to martial arts either, but it's enough of an advantage for the Big Blue to watch out for, especially bloodlusted.
Experience though definitely goes to Superman, having over 1000 years of combat experience, though the fact these both have fought some version of each other evens it out a bit
On that topic, Arsenal would obviously go to Batman, though I am unsure how some of Bat's gadgets would interact. In Post-Crisis, Kryptonians are immune to Kryptonite not from their universe, so Batman might just waste an option using that on Clark. Bruce though can get tricky with his nanotech, swarms to temporarily distract him, repair incase Superman manages to break through.
Lifting strength, I'd still be willing to say Superman edges out. Lois Lane broke the grip of a distracted Eradicator, and Darkseid was able to man-handle the armor once he got a solid grip. This is actually important thanks to how Post-Crisis Superman acts bloodlusted.
Now onto the fight; this is a bit tricky, I really haven't seen many fights where Superman cuts loose in Post Crisis, and neither have I really seen what Batman could do with the armor if he gave in to his rage. Superman usually starts off with a speed blitz + heat vision + lifting strength grip towards the Sun. Batman definitely has ways to counter, redirecting his blasts to wrestling free with his sweet two times strength advantage. Hellbat doesn't have any resistance to ice manipulation however, Superman's usual go-to when Heat Vision doesn't do the trick. It might not be much, but all Superman needs is a second of Batman being caught in the ice and the fight's being taken towards the sun. It's always his go-to when in a fit of rage, ex: Wonder Woman or Darkseid.
If Batman can keep the fight on Earth, he might be able to edge out with his superior skill and AP, Superman doesn't abuse much of his arsenal in a fit of rage while Batman would be happy to do so.
But if Superman can take the fight to the Sun, then there's not much the Caped Crusader can do. Clark's constantly getting stronger, Bruce's hits are going to be doing less, Supes would be healing faster, and he'd be getting faster. Bruce's danmaku and energy redirection can only do so much, energy absorption might only come into play a few times once Supes realizes it's not going to work to keep using it. His Danmaku at best only seemed to distract Darkseid; it's going to be doing less on a Superman actively trying to kill him and constantly getting stronger. With the constant speed + strength amp Superman could easily hold Batman near the sun, it's only a matter of time until he rips through the suit enough where he can't handle the heat of a closely burning star, or the cosmic radiations of space.
I'd probably lean on Superman 6 times out of 10.
