One of the project varieties that I am working with, Lavender, (in my experience) more often lay a blue/green egg. This is something that is being continually worked on, as well as maintaining good body size and good feather quality. On the other hand, the project Mottleds I have lay a nice blue egg. It really depends on the variety and breeder line.
The bantam Am hen I hatched and kept from your eggs last year lays the prettiest pale blue egg. I have a half bantam cornish daughter of hers too but she lays a pretty minty green egg. Love them both.