—The main approaches to high speed measurement in routers are traffic sampling, and sketching. However, it is not known which paradigm is inherently better at extracting information from traffic streams. We tackle this problem for the first time using Fisher information as a means of comparison, in the context of flow size distribution measurement. We first provide a side-by-side information theoretic comparison, and then with added resource constraints according to simple models of router implementations. Finally, we evaluate the performance of both methods on actual traffic traces.