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A rich literature in public policy studies uses public budgeting to assess public and institutional priorities and analyze how institutional or policymaking systems exacerbate or smooth budget punctuations (Baumgartner et al. 2017; Jones et al. 2009; Breunig and Koski 2006). More recently, a debate has emerged over the best way to measure the punctuated or “tailedness” of budgetary change distributions. The traditional approach using l-kurtosis of budgetary change distributions (Jones, Sulkin, and Larson 2003; Breunig and Jones 2011) has been challenged by proponents of t-scores and Gini coefficients as better measures of tail behavior (Fernández-i-Marín et al. 2019; Kaplaner and Steinebach 2022). Do these measures behave differently when comparing governing or policy systems regarding budgetary change distributions? We use data on budgetary change in Appalachia to assess which measures are best or if they matter in comparing counties and municipalities. After constructing each measure for counties and municipalities, we statistically assess how much change in ordering we observe among the local governments, comparing the measures. Our findings are important for assessing the link between theory and measurement in public policy, especially for punctuated equilibrium studies. The findings also matter for real-world governance and auditing. They offer insights into comparing counties and cities not attainable with the usual attention to geographic or population size.