Under systematic sampling with multiple random starts, one may use variance estimators based, respectively, on (1) a relatively simple design based approach; or (2) specific superpopulation models. Variance estimators derived from (1) generally will be approximately design unbiased, but may be somewhat unstable if the number of random starts is small or moderate. In addition, the performance of estimators based on (2) will depend on the extent to which the underlying finite population is consistent with the assumed superpopulation model. This paper considers diagnostics for the comparison of estimators from (1) and (2), with special emphasis on (a) exploratory analysis of the underlying finite population; (b) variance estimator bias; (c) variance estimator stability; and (d) coverage rates and widths of associated confidence intervals. Some of the proposed methods are applied to sample data from the U.S. Bureau of Labor Statistics.