After raising 4 different chocobos for digging I came to the conclusion that having high discernment does nothing for your actual digging. Without a doubt, it does help you learn abilities such as bore more quickly. However, once you have learned the abilities you want you can safely ignore discernment.
My green max discernment bore/burrow bird seemed to give the exact same items/ratios as my red low discernment bore/burrow bird (lowered discernment after learning the abilities).
As has been mentioned however, digging wouldn't bring in much gil now. It would probably take me a week of digging to max everyday just to make half the gil I would in one dynamis. Plus setting aside 70 inventory slots to dig is something I could do in 2005....but now would be impossible.