Plato and Brix (and Balling) are all the same thing - the amount of sugar dissolved in 100 grams of solution i.e. the percentage of sugar in the solution by weight. What differs between the three scales is the specific gravity associated with a given amount of sugar and that is because the three workers used different procedures to measure the SG's. If estimating alcohol content is your goal you should be using the change in extract by weight. SG point differences represent a level of approximation (SG points are not linearly proportional to extract but quite close). Whether you use points or %(w/w) you are depending on the accuracy of Tabarie's principal which is known to be less than totally accurate. Add to that the fact that you don't know your effective original gravity (because of evaporation etc.) and that you are attempting to back out extract by correcting a refractometer reading for the effect of alcohol and I think you'll agree that whether you compute the specific gravity from the Brix table or the Plato table is kind of down in the noise.
For conversion from Plato (or Brix) to specific gravity the inverse Lincoln equation: SG = 1 + °P/(258.6 - 0.876*°P) is plenty good enough. Note that if you stick Brix into the formula you will get back SG on the Plato "scale" (apparent 20/20) which is fine under the assumption that your Brix reading really represents the extract content (% w/w) of the beer (which it doesn't for reasons given above). If it did you would be on solid ground comparing the finished SG so calculated to an OG also measured at 20/20 (this means the hydrometer is calibrated to measure at 20°C and report a specific gravity referenced to water at 20 °C). See http://en.wikipedia.org/wiki/Plato_scale for details.
