I plugged Blatz's formulas into excel and got an average difference of 0.87 SG points between the two scales. Plotting Plato vs. Brix, the trend line is:

PLATO = 1.0000267*BRIX - 0.0009006

R² = 0.9999999

This was a curiosity because the refractometer conversion factor is defined as:

Refractometer reading in Brix / Hydrometer reading in Plato

I guess the refractometer conversion factor takes care of the slight difference in the scales by its definition, I was thinking that there was some unaccounted for error.

So suppose you make up a solution of water and sugar that measures 1.04003 SG, or 10 Plato. Since this is pure sugar, the Brix reading will also be 10 Brix. But if the sugars in solution are made up of more than just sucrose, as in wort, the Brix reading will be slightly higher. 10.4 if we use a 1.04 refractometer conversion factor.

Thanks for the explanation.