I don't know the exact math, and I'd be curious to see it ... but this is my ghetto math.
Area of 0ga = 53.5 mm2
Area of 4ga = 21.2 mm2
OFC = 101% IACS conductivity rating
CCA = minimum 61% IACS conductivity rating (if 100% aluminum 0% copper)
4ga OFC = 21.2 * 1.01 = 21.412
0ga CCA = 53.5 * .61 = 32.635
In otherwords, you're getting maybe 1.5x the conductivity in 0ga CCA vs 4ga OFC. I'd say go with the 0ga CCA if it's cheaper or the same cost as 4ga.
Someone do better math to explain this.