Most people on here realize I'm a pretty objective person when it comes to this stuff...so let me give it a shot. I'm going to compare each game based on Pregame Hype, Talent, Excitement, Drama, Controversy and Historical Significance.
Pregame Hype
2003 Fiesta Bowl - Miami had two heisman candidates in Ken Dorsey and Willis McGahee and were riding a 34 game winning streak into the game amid rumors that this could be the best college football team ever. Ohio State had emerged from preseason obscurity and was all but a dismissed underdog by national media. The question was never really who will win, but by how much.
2006 Rose Bowl - USC had two heisman winners in Matt Leinart and Reggie Bush and were riding a 34 game winning streak into the game amid rumors that this could be the best college football team ever. Texas held on as a co-favorite to reach the title game and, bolstered by a heisman candidate of their own (Vince Young), was a slight underdog. This game was one of the most hyped and anticipated in the history of college football.
EDGE: 2006 Rose Bowl
Talent
2003 Fiesta - 44 players (22 for each) and counting from this game were drafted in the next three drafts, including an astonishing 14 first rounders. Widely considered the greatest compilation of talent in a recent single championship game.
2006 Rose - Heisman winners and talent galore. It's ridiculous to try to project three drafts into the future, however, while the depth of talent may not be at the level of the 2003 championship game...the star power more than makes up for it.
EDGE: Even
Excitement
2003 Fiesta - Turnovers and defense ruled this game, with Ohio State only completing 7 passes. In a double OT game, there were a total of 636 yards from both teams combined and big plays were held to a minimum.
2006 Rose - Big plays and memorable runs galore. 79 combined points in regulation, 1,130 yards of total offense. Laterals and fourth down stops only added to the fun.
EDGE: 2006 Rose
Drama
2003 Fiesta - Double OT, a late Miami surge, long conversions and late flags to keep teams alive and a grotesque injury to a star all contributed to make this game (and all the fans) extremely tense.
2006 Rose - A fourth down scoring run by Young wins it, until Leinart almost gets USC back into field goal territory. I wan't even a fan, yet by heart was pumping hard when Texas was on fourth down for the game.
EDGE: 2003 Fiesta
Controversy
2003 Fiesta - Missed calls and late flags in the closing moments of regulation and OT benefited each side. Many Miami fans still refuse to acknowledge the Buckeye's victory, arguing a "phantom" pass interference.
2006 Rose - Youngs knee was down before a lateral on a TD run, but replay wasn't working in the booth, however, replay kept officiating errors from costing either team the game.
EDGE: 2003 Fiesta
Historical Significance
2003 Fiesta - A great streak was ended, an historic powerhouse was elevated to championship status after a long drought and the game earned (at the time) the highest television rating (15.0) in BCS history. Ohio State set a record with a perfect 14-0 season.
2006 Rose - A great streak was ended, an historic powerhouse was elevated to championship status after a long drought and the game earned the highest television rating (21.7) in the last 19 years of college football. It elevated Vince Young to new heights and elevated this Texas team into the argument of "The Best Team Ever".
EDGE: 2006 Rose Bowl
I went into this decision with the elements I wanted to consider...and this is what i came up with. I had no preconceived notions coming into it...and was actually leaning towards the Fiesta bowl, likely due to my own bias. While it isn't fair to either classic game to relegate it to "second place"...I have to say that this Rose Bowl may have been the best ever.