I would put my money on Barnett.
Filipovic is a very one-dimensional fighter. He's got the high kick and the stand-up accuracy. Good sprawl, but he turns into a spaz on the mat, meaning his gas tank will take a hit.
Barnett is far more tactical, experienced, and well-rounded. He's only been handed one loss in a seven-year pro career. It took Pedro Rizzo ten minutes to KO him in a fight where Barnett didn't even attempt one takedown. He wanted to stand and got a little too bold. Live and learn.
He's had to deal with heavy hands before in Rooze, Schilt, Hoffman, and Rizzo.
Mirko has looked dangerous KOing a long line of ill-equipped Japanese. Waterman gave him a lot of trouble and Nogueira - Barnett's equal in submission grappling - armbarred him the second it hit the ground.
I'd be nervous about Barnett's inactivity, but then again, Cro fighting six times this year may be more of a strain than a benefit.
Outside the ring? Barnett is representing New Japan Pro Wrestling and the angle isn't one of a UFC fighter coming in to Pride. He's signed to multiple fights and Filipovic is open to offers to work K-1 shows, meaning that any bogus reffing or judging (if one is inclined to worry about that) would logically swing Barnett's way.
Josh believes he has the high kick defense figured out. I think his absence from the US MMA scene has led some people to forget how good the guy really is. Barring any severe ring rust, Barnett via armbar in round one.