For a male and female who are equal height and weight, are ethnically identical, and who represent the center average/ median of their respective genders, are their rib cages the same size? If not, then how much different are they, and why are they different?
are their rib cages the same size?
No. The female ribcage, in addition to having a smaller volume than the male ribcage, has a proportionally narrower superior half and a proportionally wider inferior part. The shape of ribcages of women and children leans towards what older literature refers to as the thorax inspiratorius - that is, it resembles the shape assumed during inspiration (it's rounder and more convex), whereas the male and the geriatric ribcage is closer to the thorax exspiratorius.
how much different are they?
One study with a small sample size estimated that the volume of adult female lungs as typically 10–12% lower than that of males. If you're interested in actual thoracic dimensions in centimeters, please refer to table 2 of this article. Keep in mind, however, that you're looking at a study with a small sample size.
why are they different?
The study linked above speculates that the purpose of this particular example of sexual dimorphism is to accommodate large abdominal volume displacements as in pregnancy. Of course, there could be myriads of other coexisting reasons for it - in males, the extra volume could come in handy during oxygen-expensive activities such as hunting (incidentally, the average female RBC count is roughly 90% of the male RBC count). A robust ribcage also permits the attachment of stronger pectoral muscles. I would always suggest to consider sexual selection when looking for reasons for sexual dimorphism - the paradigm of "men with wide upper body and narrow lower body good, women with narrow upper body and wide lower body good" is as ubiquitous as restroom signs and the shape differences referred to in the second sentence of the first paragraph seem to fit it perfectly.
Adam Bochenek, Anatomia Człowieka I, p 291 (source in Polish)