For CNC the rounded corner means not having a sharp change in direction, which means not having to slow down to go around the corner. The rounded corner does require a bit more material to be removed. In the old days the CNC controllers would have a glitch and leave a tiny mark at these changes but I think that's handled far better now.
However, if the part can be saw-cut to the outer dimension then the chamfer is an easy feature to add.
Chamfered edges, however, are almost always easier as there isn't a need guarantee tangency that a full radius does. That said, a softer corner can be made by running a round-over tool a little above and to the outside then being off a little is not as noticeable, avoids a gouge, and looks much better than a chamfer.
Consider also - if one goes to paint the part, the smoother the transitions, the less likely for the paint to pull in from surface tension and get thinner; in chamfers it's still easy to chip paint on those sharper 45 degree transitions; it may save money later to spend a little in making the part.