The countries filed complaints against each other at the International Court of Justice (ICJ), which could award financial compensation if it finds either side violated the 1948 Genocide Convention.
The cases, filed 16 years ago, are part of the long legal fall-out from the break-up of Yugoslavia into seven states in wars that lasted eight years and left more than 100,000 dead in Europe's worst conflagration since World War II.
The ruling, which is due to start at 0900 GMT, could stoke political tensions in both countries.
"What's really at stake is both states trying to justify their wars," said Eric Gordy, a professor at London's School of Slavonic and East European Studies.
"The strongest arguments they have to say they are justifying their wars is that they were defending their citizens against genocide," he added.
The U.N. tribunal for the former Yugoslavia, which is also in The Hague, has long since ruled that genocide was committed in Bosnia, where more than 8,000 Bosnian Muslim men and boys were killed when the U.N. 'safe haven' of Srebrenica fell to Bosnian Serb forces in 1995.
Despite widespread atrocities against all sides, no court has ruled that ethnic Croats or Serbs were victims of genocide. Recent acquittals of suspects at the Yugoslav tribunal stoked anger in the two countries.
Many experts believe Tuesday's ruling is unlikely to find Croatia or Serbia liable for genocide if no individuals from either country have been convicted of the crime.
Croatia alleges that Serbia's destruction of towns and expulsion of ethnic Croats in Slavonia amounted to genocide. In turn, Serbia accuses Croatia of genocide over the expulsion of Serbs from Krajina.
In an earlier ruling from 2007 in a case brought by Bosnia, the same court found that Serbia was not responsible for genocide, but that it had breached the genocide convention by failing to prevent the massacre in Srebrenica.