I am sure there are a number of methodologies used to analyze culture. It is very important to have high alignment on culture especially if the synergies require strong integration between the companies. Here are few things that can reflect on culture:
1. HR policy and procedure. This will show how aligned they are when it comes to setting the rules for employee conduct. If one company has few guidelines and rules while the other has a library for guidelines and rules and then enforces them with a system, then you know the companies most likely will not have alignment on culture.
2. Diversity. A lot has been written about the role of diversity on culture and innovation in a group. Looking at the diversity level of the companies will show how they mostly likely to work together.
3. Age groups, while not supported, I believe a review of the age groups can be a sign of trouble when integrating cultures. This should analyzed and followed with a survey to see how well the age groups impact culture.