Hi Daryl... This is somewhat like comparing apple and oranges, IMHO. They both have their advantages and their difficulties. I do not use a router for cutting my wood box mortice, just chisels and files. You may be tempted to use a router, but I can see to many pitfalls here. For one thing, I have the area already shaped into a buttstock before I cut the mortice, so a router would not work with my method. Besides, if you did manage to cut it with a router, there would still be the fine fitting to be done afterward. A CNC could probably do it, but I am not about to go to that expense to upgrade my mill just to cut patchbox mortices... Just as fast to do it by hand when you consider setup time for CNC. Just my opinion.
Matt