I found a review of the score. Albeit it's a negative review.
This same music critic gave the X-men Origins:Wolverine score a star higher than Beltrami's Wolverine score. http://www.filmtracks.com/titles/xmen_origins.html
Wow, b/c I found Gregson-Williams score rather weak and dull. It didn't do anything for me or the lackluster movie either, imho. Eventhough I haven't heard any of "The Wolverine" score yet, I doubt Beltrami's score could be any worse. I have a feeling it'll be a step up.