There are numerous studies that look at bicameralism in public choice economics. One general conclusion is that more houses make legislation more difficult to pass, requiring a super-majority of support for legislative change. This can make Tyranny of the majority more difficult, but also lets less legislation pass in general. However, just having two houses isn't sufficient. To this end, economists would consider houses whose "chambers’ demographic characteristics [are] more diverse" more bicameral, more different and requiring a stronger super-majority to enact change.
Buchanan and Tullock, in an early look at bicameralism are concerned with the ability of a Democracy to impose external costs on citizens. They're also worried about decision making costs, the ease of making collective decisions. For example, if everyone had to agree 100% on every issue, making any decision would be impossible, but there can be no external costs imposed on unwilling citizens, on the other extreme, with a simple majority, it's fairly easy to make decisions, but those decisions can impose costs on others (Tyranny of the majority). Buchanan and Tullock find that "if the basis of representation is made sufficiently different in the two houses the institutions of the bicameral legislature may prove to be an effective means of securing a substantial reduction in the external costs of collective action without incurring as much added decision-making costs as a more inclusive rule would involve in a single house." Thus a bicameral legislature may be able help to block legislatures from imposing external costs on citizens, but it would be less of a barrier to decision making than requiring a high % of the legislature to agree before a proposal becomes law.
Another interesting study from the public choice literature is summarized below
Bradbury and Crain (2001) examine the discrete difference between
bicameral and unicameral systems in different countries. Specifically,
this study examines the effect of the bicameral institution on
redistributive spending due to the "Law of 1/n," which is pork-barrel
spending fueled by an increase in elected representatives. The study
finds that countries with bicameral legislatures experience less 1/n
spending than unicameral countries, which is consistent with the
hypothesis that adding a second legislative chamber limits
One literature review can be found at The Encyclopedia of Public Choice, page 39, quoted from above. Also see the literature review from Constitutional Political Economy in a Public Choice Perspective section 8.5.