To Thanos is Awesome:
They're what if stories, essentially, with characters used in characters, from the very people who write said characters in canon stories, so we can base our observations on these. It's the closest thing to canon we're gonna get anyways.
I certainly agree, give Bats access to his utility belt and things get more even, though, to be fair, Steve should have access to his shield as well. As far as pure h2h, Cap would win, after a long, exhausting fight, even for a Super Soldier such as he.
The vast majority of crossovers(with marvel and/or DC at least) are not canon to the main universes(616 for marvel).
I would go into detail on why Cap would win, easily, against Batman, but considering that I've already done that in a few other threads, with that exact topic, I really can't be arsed.
Do you have anything to back up the claim that Batman's more skilled than Daredevil?
I'm sorry, but your own perception on "who's on the list" has absolutely no relevance in the debate at all. The fact is that Daredevil's fought and beaten Marvel's top martial artists. If there's a person he hasn't beaten on the top list, it's because Daredevil hasn't fought him or her.
Are you serious? Daredevil's fought so many more superpowered/master martial artists than Shiva that it's not even funny. the experience factor goes to him by a LARGE margin. And when has Daredevil been beaten by people less skilled than himself? Anyone who's beaten him, he's returned in kind at some point or another. Also, Lady Shiva simply hasn't been in as many fights as Daredevil (has she ever had her own series even?) so of course her record's going to be more consistent. That's like saying someone who's won 1 out of 1 boxing match is better than someone who's won 47 out of 50, just because 100% is greater than 94%.
And who has Lady Shiva beaten? You want to compare her records to the best martial artists in DC? She's lost to Cassandra Cain twice, Batman, Tim Drake, David Cain, Cheshire, Prometheus, Victor Sage, and Richard Dragon. Daredevil's beaten Captain America, Wolverine, Iron Fist, Black Panther, The Punisher, Spider-Man (including once with the symbiote suit), etc.
Wait... You're listing who Daredevil has defeated, but you're listing who Shiva has lost to? How exactly does that give any kind of comparison?
Listing who the two have defeated, respectively, would make sense to a certain point. As would listing who they have each lost to. But the way you're doing it, is like comparing apples and oranges. Not to mention that no context is given, for any of the mentioned fights on either side.
People also seem to be forgetting, that Daredevil is the protagonist of his own title, while Shiva is not even a primary villain.