I found that many atopic dermatitis research used female mice rather than male ones. I wonder the reason why they prefer female ones.
Of course there are differences. Many genes respond to androgens or estrogens, which are sex specific nuclear hormone receptors that regulate transcription. Female mice are easier to house and don't fight when caged together. Males are ok if they are with littermates and no females, but otherwise they can fight and cause serious injury. Most NIH studies now ask for males and females to be included even for mice.
We used only female mice to look at various skin cancers and skin infection disease. Our reason was because the males kept fighting and barbering, resulting in damaged skin that can not be used for the research.
Since female cycles menstrually or esrually (in mice) and is under the effect of hormones throughout, in that case if you want to be independent of changing hormonal effect, you may choose to have male animals for experiments. If you are doing breast cancer experiment, you should choose female animals. For my orthopedic experiment where I transplant cartilage in osteoarthritic knee, I chose male rats.