I'm an active offensive line coach, and I'll give you my take on the two schemes.
Zone Blocking schemes in general lead to more big run but also more stops for 1 yard or less and a lot more runs for losses. You want smaller, quicker offensive lineman, who can help double team a DT, and then one releases to pick up a LB at the second level depending on the type of run. All in all, this is probably the better running scheme, but its much harder to find lineman who can truly do it effectively.
Man Blocking schemes in general have less huge runs, but have far higher 4+ yard run percentage. You want bigger lineman who can drive, pummel and destroy any size lineman, with just enough athleticism to hit LBs at the second level. It's much easier to find these types of lineman.
The Cowboys have no chance at switching schemes. Kosier and Free could do it, but Gurode, Bigg, and Columbo have a 0% chance of being successful zone scheme linemen.