Or, for purposes of the test, why not simply use the same conventional acid fixer for both? If the question is about whether stop bath stops development faster than water, it's obvious it should -- acidifying chemistry that only works in an alkaline environment is faster than simply diluting it until you can't detect the reaction rate. What happens in the fixer should be pretty much the same (at least for the first negative in fresh fixer) after the stop or "water stop" step. If you're that concerned about it, give both negs a second bath in acid stop so they enter the fixer in the same condition.
However, there are other considerations -- an acid stop used with a carbonate alkali developer runs a risk of gas generation damaging the gelatin, but once the stop (or short wash) is completed, there's still the question of whether to use acid fixer or neutral/alkaline fixer. It's been strongly asserted, with what seems good chemical basis, that neutral to mildly alkaline fixers and, indeed, an all-alkaline process are better for emulsion, but there may still be a need to precisely stop development.
One suggestion I've seen is to use a lower pH stop bath with a buffer providing a reserve of acidity -- sodium acetate buffering an acetic acid bath will have lower pH than the common 1.3% acetic acid stop, yet has (potentially, depending on concentrations) much larger reserve of acidity against neutralization by alkali carried from the developer, and is less prone to form gas on reaction with carbonate (because it's less strongly acidic). In fact, I wonder if it might not be possible to use unacidified (and thus very mildly alkaline) straight sodium acetate solution as a near-neutral stop -- still stopping the development, but without an acid that can change the gelatin state.
