Cross of Brown X Blue is not going to give precisely the same result as crossing Blue X Brown. Reciprocal crosses are affected by the W/Z chromosomes as some of the genes in the porphyrin biopath are on the sex chromosomes.
That said, you can still generalize that crossing a blue egg layer X a brown egg layer and carrying forward to the F2, 1 in 16 will lay white eggs, 3 in 16 will lay some shade of brown egg, 1 in 16 will lay some form of blue egg (caused by recombination of the blue and white genes where the white gene disables the porphyrin biopath), and 11 in 16 will lay some form of egg carrying the blue egg gene with varying overlay of porphyrin producing olive green, teal, spearmint green, tan green, or other slightly nuanced color on top of the blue egg shell.