Looking long term, I go with Beasley. He's younger and provides much needed bench scoring, something Odom cannot do as well. Granted he does not play respectable defense, but I feel like a couple of games with Kevin Garnett will help him pick it up.
If we decide to make one last run for a championship, I go with Odom. He has no upside, but you know exactly what you'll get from him. A guy who can excel at running play sets, dribble like a point, and bang like a big. He can help with rebounds more than Beasley and is better overall.
If I were to choose only one or the other, I would go with Beasley. He has too much potential, and would be better to pair up with Rondo than Odom.