Probably not true, but only just. 570 men die of breast cancer each year in the US (latest stats from the Cancer Statistics Center) while 330 people have died in mass shootings in the US this year so far. You can see the stats, taken from the Gun Violence Archive, here: https://docs.google.com/spreadsheets/d/1xB5VWgcpvw5UrWYq-6so...
Mass shootings are more traumatic though as they're extremely brutal, graphic, and sudden. I'd weight the actual impact of someone I know being shot in a mass shooting far worse than someone I know dying of breast cancer. The latter won't have them leave in the morning and not come back at 5pm randomly. It also won't create a general climate of fear, distrust between people, and terrible politics. Both are tragic, but tragedies of different kind, which is why direct comparisons always seem technically correct but missing so badly the way people actually think about and experience tragedy.