I can't speak to non-economic history, but Tilly is quite influential in the literature on state capacity and the fiscal military state. North, Wallis and Weingast's recent book "Violence and Social Orders" is, at its core, a response to and elaboration on the basic Charles Tilly thesis, as is Philip Hoffman's "Why Did Europe Conquer the World?" It has also been very influential in comparative Europe/China studies, notably through the work of R. Bin Wong, although they have been as much critical of the export of Tilly's model outside a European context. Others, including William Guanglin Liu, have used Tilly more positively in the Europe/China comparison.

This doesn't necessarily imply that his work is accurate as a description of Europe itself, though it seems to be held in high regard in Economic History generally. But the ideas have been influential.