In the measurement field of international nuclear safeguards, passive neutron coincidence counting is used to quantify the spontaneous fission rate of certain special nuclear materials. The shift register autocorrelation analysis method is the most commonly used approach. However, the Feynman-Y technique, which is more commonly applied in reactor noise analysis, provides an alternative means to extract the correlation information from a pulse train. In this work we consider how to select the optimum gate width for each of these two time-correlation analysis techniques. The optimum is considered to be that which gives the lowest fractional precision on the net doublets rate. Our theoretical approach is approximate but is instructional in terms of revealing the key functional dependence. We show that in both cases the same performance figure of merit applies so that common design criteria apply to the neutron detector head. Our prediction is that near optimal results, suitable for most practical applications, can be obtained from both techniques using a common gate width setting. The estimated precision is also comparable in the two cases. The theoretical expressions are tested experimentally using 252Cf spontaneous fission sources measured in two thermal well counters representative of the type in common use by international inspectorates. Fast accidental sampling was the favored method of acquiring the Feynman-Y data. Our experimental study confirmed the basic functional dependences predicted although experimental results when available are preferred. With an appropriate gate setting Feynman-Y analysis provides an alternative to shift register analysis for safeguards applications which is opening up new avenues of data collection and data reduction to explore.