A commenter on one of the links nailed my concern: "Isn’t there selection bias in the party unity scores for the Senate? Because of the threat of the filibuster, Reid wouldn’t move most bills to the floor without the assurance that he has a high degree of party unity. The more moderate members would hold out, initially, until concessions were made. The higher unity score isn’t just a product of Democratic cohesion, but the impact of increased use of the filibuster by Republicans." It appears the majority party typically has higher party unit, consistent with the idea that this is driven by the fillibuster threat (both from D and R).