If the Cavs weren't going to offer anything more than a contract to finish out the season the rest of this year, then of course Hudson made the right move to move on (played with Memphis before, it's his hometown, he has a shot to play in the playoffs if Arenas/etc. are hurt, might get seen by more teams in the process).
It surprises me that the Cavs didn't lock up Hudson for the rest of the year (as they did with Sloan) when they had the chance after his first ten-day contract. That short-term decision was strange to me. But I don't think the Cavs made a bad long-term decision yesterday. He also hasn't played as well over the last 10 days. I imagine they offered to keep around for the rest of the year (why wouldn't they?) but when they wouldn't make further guarantees, Hudson had a much better offer waiting (at least in the short-term) with Memphis.
As someone said above, it wouldn't be surprising to see him back fighting for a job with the Cavs somewhere down the road.