I would rather Ariza than Battier.
I think Ariza's quickness and athleticism would be a great addition to the Celtics. It would be fantastic to see Rondo have a wing who fills the lanes like Ariza does.
Furthermore, Ariza is the better all-round offensive player due to his superior play in transition + cutting ability + offensive rebounding + ball-handling ability. Ariza is also a better rebounder and provides about 80% of what Battier does defensively. Add in the young age and Ariza's ability to be a long term fixture here in Boston, and, I think Ariza is the clear winner.
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That said, I don't see Houston trading Ariza or Battier for anything other than talent. So the Sheed for one of them proposal, I don't think that has any legs.
I expect the Rockets will ask for Kendrick Perkins in return for either player.