Yes, CCM 6.1 is stable enough for new deployments. There were many bugs in 6.0 but these have been fixed in the new releases. I wouldn't roll out 4.1(3) as it has been announced as End of Life. The feature sets in 6.1 really add alot of nice functionality over 5.1 so I wouldn't go with 5.1 either :)
We just moved from 4.1.3 to 6.1.1, the only issue we have found is Attendant Console's ability to connect has been buggy. We are still working with TAC on the issue, but basically it takes 2 full minutes to find the server and log in, then never populates the directory with status.
Other than that, its very nice. Administration is faster and the expanded feature set is worth the effort.