How have anthropologists traditionally differed from political scientists in their approach to the political?
Anthropologists argue that their view of the political differs from that of political scientists. However, this difference may well be overstated. It is more of a matter of degree and not a truly qualitatively difference.
To see how anthropologists perceive these differences, let us look at Chapter 8 in the 14th Edition of Cultural Anthropology: Appreciating Cultural Diversity by Conrad Kottak. There, Kottak tells us that the way that anthropologists look at politics is
…global and comparative, and includes nonstates as well as the states and nation-states usually studied by political scientists.
What Kottak means here is that political scientists study governments while anthropologists are more likely to look beyond governments. When anthropologists think about the political, they think about other ways in which power and authority can be wielded. They think about these instances as part of politics while (Kottak implies) political scientists only think about politics in terms of actual governments.
I would argue that this is not really true of political scientists. They do, at times, study politics in nonstate environments. However, it is true that political scientists are more likely to focus on the official political mechanisms of the state.