In this paper we study the dynamics of self-adapting systems. Our main objective is to compare adaption dynamics of similar systems, i.e. systems that differ only in their organisational networks. We specify adaption in the formalisms of Hornets – a formalism that uses nets as tokens, i.e. they follow the nets-within-nets approach. We identify different abstractions of the reachability graph that focus on the adaption aspects of the processes. We develop key measures for adaption processes on these abstracted graphs. The key measures are used e.g. to compare two variations of the same adapting system. The approach is illustrated by a case study: We analyse a Hornet-model of Axelrod’s well-known tournament where the playing agents adapt their strategies during the game.