I would have preferred Stastny or Toews, but Sutter does fit in well.
He's similar to Bjugstad, in that he's decent defensively, but not good enough to be a proper matchup C. And despite having some very nice tools, he lacks the toolbox to be a top 6 option. 2 years off also isn't going to help that, but still I could see him being a decent defensive 4th line centre.
I remember Pittsburgh back in the day trying both as #3C back and not getting the results they wanted. Hell another former Oiler in Sheahan also went down that path.