In my experience it can work both ways.
There are quite a few genes involved in brown eggs. As the indivdual genes have not been properly studied, as far as I know. If they were I'm not sure how one would tell the individual effects apart.
I've found in the first cross the eggs can get considerably darker. It seems logical to suppose that perhaps some of the dark egg genes were dominant, or incomplely dominant, & some carried by one strain were not exactly the same as the dark egg genes carried by the other.
It is also logical to guess that those genes would be heterozygous in these birds. Thus in the following generation those genes would start to segregate giving some with lighter egg colour than either of the original colours. Also one would get some with darker egg colour than either of the originl colours.
Well this my hypothesis to exaplain what I have observed in my birds.
When messing with different colours I've found it important to trap nest & keep records of the parents of each individual bird.