Rogue isn't magical... she'd win.
Besides Black Alice wins, she can steal any magic characters powers. If they are not in the vicinity she would get powers from any one of the magic based characters in the DC Universe and they are all pretty powerful.
This is actually an interesting fight. Against any magic-based character, basically Black Alice wins - it's not even a contest. Against a non-magic character, she still has access to steal any magic user's powers. However, against Rogue? If Rogue is able to manage to touch her, then she'd have Black Alice's powers plus her own.
Overall, I'd give it a slight edge to Black Alice, but Rogue can very well quickly turn this around and win.
I think Rogue stealing her powers would depend on whether or not Black Alice is truly a magic user, or a meta-human that just has the ability to steal magic users powers -- and then Rogue would be stealing her direct power. I don't know a whole lot about BA, but she's got three threads I have found so far on page 1...she seems pretty powerful.
Alice's power is to steal magical powers from other magical beings. If Rogue has no magic, then Alice is still a normal human. However, Rogue has still got that siphon touch that can render someone incapacitated or dead, right? So it should be safe to say Rogue wins.
Alice does not need to be anywhere near a magic user to steal their powers. Rogue's powers depend on contact. There are plenty of magic users whose powers Alice can steal or has already stolen (like Dr. Fate, Zatanna, Wonder Woman, Captain Marvel, Etrigan, Nightshade and so on) and then use those powers to defeat Rogue before she even gets close.
Much as I hate to admit it, Black Alice will win this. Lori (Black Alice's real name) can steal powers from ANY magical being. If there's no magical being around, she steals from a random magical being. She's stolen powers of Wonder Woman when Wonder Woman wasnt even around. Same for Captain Marvel, Zatanna, and Dr. Fate. And she's stolen powers from Dr. Fate and Zatanna so often that she's gotten pretty good at using their powers. And people like Wonder Woman have powers which are not particularly difficult to understand.
God help Rogue if Black Alice was to steal Spectre's powers or Juggernaut (Juggernaut being someone Rogue's been unable to siphon the power away from, and Spectre being someone who could kill Rogue with a snap of his fingers)
Black Alice is ridiculously overpowered. Rogue would not stand a chance. Unfortunately. Because I really prefer Rogue.
Lol, so everyones basically saying Black Alice is going to be like to Rogue-
Black Alice-I don't have any powers right now, so i'll be right back.
*Goes to get powers*
*3 hours later*
Black Alice-I'm back, and I got power that can one-shot you!
Rogue is it Batman? Squirrel Girl? Karate Kid?
Black Alice-Nope, it's Doctor Fate's
*Black Alice one shots Rogue*