I thought I’d already left a note on this but it must not have posted. The Brown cockroach and the American cockroaches look similar, with the exception of the characters that Ross mentions. Both have a pattern on the pronotum, with the dark-light contrasts of the American more vivid (on average) than seen in Brown cockroaches.

This specimen has no real variation in the color of the pronotum, which is very dark. This is consistent with the Smoky brown cockroaches. If you did count the subtle changes in color on the pronotum of this specimen (visible because it is a good photograph) the pattern is actually reversed of what you would expect. There is a large degree of variation in colors for Periplaneta cockroaches, but this one fits fairly securely in with all of the Smoky browns that I have seen. The pattern of a Brown cockroach is much closer to an American cockroach. This one is in the spectrum I would expect for a Brown cockroach: