Hello Colin88,
Why don't you have a look at: "Survey of CGS vs PCGS/NGC Grades", which was started by Sword in this forum section on 20 Septe4mber 2015?
I think the info you're seeking to find is presented in that posting for Victorian halfpennies. My contribution to that discussion uses actual graded results of the three TPG services of interest to derive the equivalences for that series of coins that were graded by CGS, PCGS, and NGC. Such a comparison can be made for any other series of coins by a similar treatment of the three service's population census data.
It must be emphasized that the equivalences made only apply to the Victorian halfpenny data that was published at the time of comparison AND apply to the overall results, which are NOT necessarily applicable to a coin-to-coin comparison for equivalence!
This topic (and TPG results, in general) is a thorny issue, but coin grading will never be an exact science with a fixed set or rules to follow because the preferences of the graders determine the results. (The degree of preservation (the definition of "grade") will always depend upon the grader's personal preferences for such elements as depth of strike, edge conditions, coloration, surface blemishes, toning spots, degree of wear, etc.). Only gross comparisons can be applied with any degree of confidence!
Cathrine