With a certain exception, a chicken inherits one gene from each gene pair from it's father and one from its mother. From that aspect, mother and father contribute equally. That can be egg laying, body configuration or size, or eye color. From my experience a rooster contributes as much as the hen as to whether or not the pullet will go broody, but that comes from knowing that his mother went broody a lot.
The exception is the sex linked genes. A rooster gives one copy of one of the genes at each gene pair to all his offspring. A hen is not so generous. She gives a copy of one of the genes she has at each "gene pair" but with her they are not all pairs. The sex linked genes are single genes where a pair should be. She does not give a copy of anything of these sex linked genes to her daughters. The absence of one of the genes at those sex linked genes "pairs" is what makes the difference between male and female. Unlike mammals, with chickens it is the female that determines the sex of the offspring.
Some of these sex linked genes have nothing to do with male or female traits. The barred gene for example. That just has to do with feather pattern, whether male or female. There is one that has an effect on the shade of brown on a brown egg. There are a lot of different gene pairs that affect brown shell color, only one is sex linked. But in this case a rooster can have more effect on the shade of brown than a hen if he happens to have that gene.
So it is possible a rooster can have more of an effect on his daughters than the mother, but the mother will not have more of an effect on sons than the father. They both contribute equally to their sons.
Even if they don't have more of an effect, they can have more of an apparent effect. Roosters do not lay eggs. If you know what kinds of eggs his mother and his grandmothers laid, you can infer what kinds of genes he might contribute to egg laying. But you can see what egg a hen is laying. You can more readily see what she is contributing. Same thing with body configuration. Due to their sex they have different body configurations even with the same general genetic contributions. If your interest is body conformation or even size for a cockerel to butcher, the father is a better model to go by than the mother, though if you know something about her father and grandfather you can draw some inferences.
I don't know if this makes sense or not. Basically a hen and rooster will contribute genetically the same as far as any traits go. I consider the sex linked contributions as really minor, in most cases inconsequential. A rooster from a really great egg laying line will greatly contribute to egg laying. Same with a hen from a great meat line. But since roosters don't lay eggs it is often better to select certain sexes for certain traits unless you have some really great historical records about their parents an grandparents.
