KR,
Codec adaptation : to increase the signal protection, to allow a good voice quality while suffering from a poor C/I
Channel adaptation : to maximize occupancy of the cell by making an intracell HO from FR timeslot to HR timeslot.
Both of your answers are good. Why should there be only ONE advantage for this feature ? All in all, it increases interference robustness + cell capacity, depending on the situation the call is facing, and depending on the cell load status.