Akos Lada has a new research paper (pdf) on this question:
Does sharing the same religion, civilization or racial proximity lead to more peaceful relations between countries? This paper argues that cultural similarity can actually cause wars, which occur to combat diffusion. This new theory of war combines the models of Acemoglu and Robinson (2006) and Fearon (1995), and shows that cultural similarity can lead to more warfare when old elites are afraid of losing their position to a newly inspired citizenry, as these elites try to destroy the external source of inspiration. The microfoundation for inspiration is derived from revealed information about the income level under given institutions, which are assumed to have positive correlation with cultural proximity. On the empirical side, I present case studies on the 1848 Revolutions, the 2013 Korean Crisis (using content analysis of official North Korean articles) and on the First World War, as well as statistical analysis on all the wars of the last two centuries.
Here is Lada’s blog post on Ukraine and Russia. Excerpt:
Perhaps because a more democratic Ukrainian government may serve as an example to Russian citizens of how culturally-similar people can be alternatively governed. As history shows, a dictator with an army does not wait for this to happen.