It is an oxidation in alkaline environment. As persulfate decompose in sulfate and hydrogen peroxide you can shift to these compounds in correct ratio; So 1 mol of potassium persulfate can be shifted to 1 mol of nydrogen peroxide and 2 mols of potassium sulfate.
The original question concerned persulfate and bisulfite for total nitrogen determination. This question is now different (concerns total P). Don't know for sure what question you want answered. However, the two S compounds in the original question have S in two completely different oxidation states. Hence, they will have very different oxidizing abilities. It is not likely they will function in the same way. If you want an accepted analytical result, you should use standard analytical procedures.
Molybdenum Blue Method is excellent for total phosphorus measurement (detection limit 2ppb)
You can not substitute bisulfite for persulfate in any method that involves an oxidation reaction. Persulfate is a strong oxidant whereas bisulfite is a reductant.
The first question is: in which matrix do you want to determine total phosphorus?
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