What underlayment should I use to reduce traffic noise under a hardwood or bamboo floor?
You probably missed "the best option for reducing noise to below" if you put down new subfloors and didn't put insulation under them (assuming you actually removed the old subfloor and had open joists.) Your next-best option would be to blow in insulation from below.

If you are already committed to nail-down flooring, I don't think the underlayment will make much difference, as the nails will transmit sound into the structure. An actual floating floor on the thin, dense foam underlayment sold for that purpose would be the best option on top of the subfloor for traffic sound reduction - or a "no shoes on the second floor" house rule.