They're both known for their tempers. In fact, outside of their professions, their tempers are what they're known best for. Sometimes when they fight, the crew members in neighboring quarters call security on them, which usually ends with each trying to convince the security officer in question to back them up.
Rumors swirl around the ship about them, speculation over why they're even together when they fight so bitterly. Stories are traded of their more public altercations - the one in Sickbay where Nurse Ogawa had to ask Ro to leave, or the one in Ten Forward which ended with a glass of Saurian brandy shattered against the bulkhead, or any of the nearly countless others.
What the rumor mill wasn't privy to was the fact that, although outwardly vitriolic, the fights between Beverly Crusher and Ro Laren were, largely, for fun. A form of emotional exercise, something to get their adrenaline spiking, their blood pounding... and their libidos racing.
The complaints from their neighbors continued long after the fighting ceased.