I'd like them both, because I feel that if we got the two of them, we would be a contender, despite both's free throw shooting. I really don't see how the Pacers nor the cHeat could match up against both Monroe and Asik as well as Sully. But that's probably a pipe-dream.
If I had to choose one of Monroe/Asik, it would be Monroe. Monroe is a VERY intelligent player. He could learn to play D and so still has upside.
Asik is 4 years older, and while both rebound at a comparable rate, Asik pretty much is what he is: a tough, physical center who bounds and plays good D.
They are the same size, but Monroe can score. Put him next to a frontcourt-mate like Sully who can pass and RR who will get him the ball where he wants it all the time, and he could be a dominant offensive force.