They'd fight for comic book reasons. Somebody's a clone, or mind-controlled, or from an alternate reality. Whatever sells more issues. Two heroes being friends has never stopped fan battles before. Why shouldn't they fight?

Depends who the writer needs to win in their story.

I want to know how is more skilled Batman or Katana because she has killed quite a few villains with that sword.

Batman normally puts a stop on anyone killing people like that.

Which villains has she killed with that sword?

She use a sword really didnt know that interesting?

Yeah

"Why would they fight? They're friends."

Simple: SPARRING!

Katana uses a sword called Soultaker they state it might have a curse like the famous blade masamune.

Soultaker absorbs the souls of people killed by it , and it houses one important to Katana her dead husband.

This sword according to legend wants the user to slay to absorb the souls a evil act.

I know about the Soultaker. But which "quite a few villains"?

Oh