Batman is slightly more skilled at h2h than DD, and Lady Shiva is marginally more skilled than Batman.
When people think of Marvel's top 5 martial artists, DD isn't on the list at all.
When people think of DC's top martial artist, Lady Shiva is often regarded as the most skilled.
And yes, she def. Has more experience.
She's consistently doing well against martial artists near her level, despite very few mishaps. while DD is so inconsistent that it's hard to pinpoint his skill level. Sure, he's done well against BP and Cap and Iron Fist but he's oftentimes defeated by people considerably less skilled than himself.
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.