All this 3-4, 4-3 stuff is nonsense. First, good DCs out there are not running pure 3-4s or 4-3s. Second, there's likely no such DC currently employed by an NFL team who doesn't know how to run both. If he doesn't, he doesn't take his career seriously, which would be unprofessional.
That said, if you held a toy gun up to one of their heads, they'll definitely have an opinion on what they think is the superior scheme. But, this may change based on personnel.