It will actually now be up to Wolvie himself, Hugh Jackman, to make the call on who wants bossing him around for a few months. Vulture's report is that he'll be meeting with both Slade and Schwentke, but that their tipster pins Slade as being a foregone conclusion. That's a great choice in my book, as I've been a big fan of the British director's work since Hard Candy (hell, he even managed to make a not-terrible Twilight movie). but even if it didn't go to Slade, I've yet to see anything of Schwentke's that makes me think I want him to make a superhero action movie (hopefully Red changes my opinion on that front).
Plus, my preference for their past films aside, I think Slade is the better choice solely because a Wolverine movie set in Japan is going to require a bold visual style; a style I've yet to see Schwentke execute properly. That's just me though. Who would you like to see direct the next Wolverine?