I've dug up both & from my experiences, I think you're in for more work of about the same caliber, possibly more if your Nandina is the kind that forms lateral shoots right under the soil surface. I've dug more Nandinas than azaleas but from what I've seen, leaving some azalea roots won't result in the azalea growing back, but leaving Nandina roots will result in new growth sprouting from them.
If I ever have the task of removing a Nandina again, I will put a hard smother over the spot after the excavation for about a year, something much stronger than cardboard, like a piece of sheet metal, because I've never successfully gotten rid of one by just digging up all the roots I could find one time, it's always required repeated efforts.