Coaching: Ohio State's coach is Jim Tressel. His game plan typically emphasizes defense, conservative offensive playcalling, lots of punting, etc. He has been coaching since 1986, has been the Head Coach at Ohio State since 2001, won a national championship, and his job is secure. The Rose Bowl is a BCS bowl but is nothing for the program to be excited about, having been to three national championship games since 2001.
This is Chip Kelly's first season as a head coach. He has been the offensive coordinator at Oregon since 2007. His attack led the Pac-10 in his first season in points scored. This bowl game is seen as a step up for Oregon, and is their first BCS bowl since 2002.
The motivation factor will be on Chip Kelly's side. It is his first bowl game and he will be more interested and motivated.
As far as technical knowledge, I believe there to be a diminishing return to experience and knowledge. While Tressel has the advantage in preparing his team for bowl games, its unclear to me how much of an advantage it is.
Ranked Opponents: I am a firm believer that the ending ranking, not the midseason ranking, indicates the true skill of a team. For example, USC was ranked #4 when they lost to Oregon, but have clearly proven to college football followers everywhere that they are not the fourth best team in the land.
So lets look at their ranked opponents and how they played against them:
Oregon lost to #6 Boise State, beat #23 Utah, beat #24 USC, lost to #21 Stanford, beat #20 Arizona, and beat #18 Oregon State. Also of note, they beat Purdue.
Ohio State lost to #24 USC, beat #25 Wisconsin, beat #13 Penn State, and beat #10 Iowa. And they lost to Purdue.
Here Ohio State has the advantage of beating two highly ranked teams (Penn State and Iowa) but Oregon has played half their season against ranked opponents (tougher average schedule).
Common Opponents: Oregon and Ohio State played two common opponents: USC (home games for both teams) and Purdue (home for Oregon, away for Ohio State). Oregon won both games and Ohio State lost both games. This seems like an important detail. Especially the USC game. With hindsight we realize USC was lucky to upset Ohio State by scoring on a last minute touchdown.
Schematics: Ohio State and Jim Tressel have struggled against the option and spread in the past. Look at their performance this year against Navy, and Florida in the national championship game. Also, Texas when they had Vince Young. Oregon has a fast, small, and athletic group of scorers who thrive on open field running. Ohio has struggled in the past against these teams.
Oregon has this season handled physical teams with mixed results. They lost to a fired up Boise State team in Idaho and to a physical Stanford team. They did however beat USC easily and handled their difficult schedule with aplomb.
Stadium: I anticipate the Rose Bowl being a home game for Oregon, as it is their first trip in many years there and Oregon's proximity to the Rose Bowl (relative to Ohio State).
X-factor: Ohio State has lost three straight bowl games. Jim Tressel won't want to graduate a class that hasn't won a bowl game.
Secondly, Ohio State has lost three players due to academic ineligibility.
Conclusion: Oregon has the bulk of the advantages.