IMHO, I'd say neither. Pr numbers are of the same order of magnitude at equal temperatures. Apparently, it all depends on the flowing conditions at equal temperature and pressure.
When comparing air, ammonia, carbon dioxide, helium, hydrogen, and water vapor, all athe same T, P conditions, and using Sieder and Tate findings, I came to the following conclusions:
For equal Re, the dominant factor is the thermal conductivity. Thus, hydrogen would have the largest forced convection htc.
However, for equal gas velocities carbon dioxide and water vapor (depending on temperature level) seem to be the best in this group because they show a much larger Re, counterbalancing hydrogen's larger thermal conductivity. Again, all these thoughts are based on Sieder and Tate measurements and published graphs thereof.
If radiation from the hot body is also a factor, since diatomic gases are, more or less, diathermic I'd say carbon dioxide would have to be picked up as coolant among the others. Corus, do you agree ?