I think your perception is correct, but I am no expert. I sense that evolutionary psychologists are really interested in human universals: the famous experiments of Tooby and Cosmides go right to that point. Why are we all afraid of snakes? Why are our babies do hard to toilet train? But they generally don't have a lot to say about variation among humans in these traits.

The other sort that you and I both perceive are interested in human diversity and aren't much concerned with the bigger questions of the ev psych people.

No, they don't "play nice" with each other mostly. It is an exaggeration to say that each regards the phenomena of the other as nuisances. They certainly should see different things: C&T see evolved cheater detection in a logic game while psychologists of the London school see G playing itself out in the diversity of correct answers.

The two areas will come together soon: they are already starting. As some of the comments here indicate, we can't really understand what "Neanderthal intelligence" might mean until we understand the evolution(s) of intelligence. We can examine data all day and still have not an iota of insight about that bigger issue.