A bunch of factors to consider in selecting a radiator.
1. Corrosion. Iron has an electropotential of 0.441v, copper -0.345v, aluminum 1.300v. The bigger the difference (iron/copper .786v, iron/aluminum .859v) the more likely for corrosion. The key here is to use a proper anti-corrosion antifreeze.
2. Core Support. Ford radiators of the 1932-1939 era had a steel support structure which supported the grille and hood and fenders to some degree. If the radiator manufacturer cheats the radiator will break. The manufactures of the cheap aluminum radiators do not seem to understand or care.
3. As noted by Aussie Merc the stock radiators had a large upper tank which received any overflow and acted as an air baffle. If an aftermarket radiator does not have these an overflow tank and possibly an air baffle will need to be installed.
Regardless, with the right structural engineering, right coolant, and right recovery system either aluminum or copper should work. with the wrong... failure.