Let me say first off that I don't know anything about cognitive style. However, I have recently read an interesting article by van Knippenberg and van Ginkel (2010) about diversity in work teams which might be relevant here.
To explain the sometimes contradicting effects of diversity on work teams, the authors propose a model that differenciates between two types of diversity, demographic and functional diversity. According to the authors, these two forms of diversity have opposing effects. According to Self-Categorization Theory, demographic diversity (age, gender, country of origin, etc.) is likely to initiate categorization processes (see this post for more information) through which people perceive themselves as belonging to different groups. These perceptions of ingroup and outgroup might lead to conflict and thereby negatively impact team performance.
Functional diversity on the other hand refers to different areas of knowledge and expertise, that members of a team might have and is seen as an informational ressource. A team with experts from different fields has a potential benefit (at least with regard to some tasks). This might also cling to cognitive style. This kind of diversity, then, can potentially increase a team's performance. However, it is not sufficient for a team to be functinally diverse. Rather, the members have to put this diversity to use by elaborating together on the task at hand. This Elaboration process is not automatic and involves the exchange, discussion and integration of information.
The Categorization-Elaboration Model of Work Group Diversity
It is important to note that according to van Knippenberg & van Ginkel (2010), it is not the question, which one of these two approaches is the correct one. Instead, both kinds of diversity might be present at the same time and interact, leading to the often mixed results from studies on diversity. There are a couple of moderators in the model, as well. Task complexity is thought to be a factor with regard to funtional diversity: the more complex the task, the more schould the team benefit diversity. The two other moderators are motivation and ability, which are, as I would argue, not specific to the discussion of diversity.
Team Design and Management
What can one learn from this with regard to the design of work teams? The first thing that comes to mind is that teams should be functionally diverse. In addition, the importance of the elaboration process needs to be acknowledged, because otherwise informational ressources will not be put to good use. As to demographic diversity, the suggestion cannnot be to have teams not be diverse (to prevent categorization as ingroup and outgroup). Rather, the authors suggest to foster the importance of group members beliefs in the value of diversity. van Knippenberg & van Ginkel also prevent evidence that leaders can be trained in order to do so.
Van Knippenberg, D., & van Ginkel, W. P. (2010). The categorization-elaboration model of work group diversity: Wielding the double-edged sword. In R. J. Crisp (Hrsg.), The psychology of social and cultural diversity (S. 257–280). Malden, MA: Wiley-Blackwell.