I think it depends on the helmet as much as the shape of the head. My Kask sits really low in the front, so all it wants to do is push the brim of the cap down. My old Smith was somewhat more cap friendly.

I have a selection of cycling caps because for the mountain ascents, the helmet gets strapped under the saddle. No point in wearing it when my average ascent speed is about 8mph. Cycling cap on the way up, helmet on the way down.