Honesty, I feel Rome and Parthia could be friends, or at least stay normally friendly with each other. Anything would be better then the endless tug of war Rome (Later Eastern Romans.) and Persia seem trapped in OTL, and that pretty much doomed them both. Anything that can reach a long term truce and status quo ante and stop the destruction of the later wars.
Both the Romans and Parthia can reap the benefits with all the saved money that was being pour into their eastern/western borders. It would help Parthia won't be anything like the OTL expansionist, militarist Sassanids, at least for a good, good while with them as Flavius pointed out the Arsacids would push for peaceful relations and a Roman Emperor that seeks the same and don't go on foolhardily wars.
Rome could be saved from the worst of the Crisis of the Third Century, downsizing it as Flavius pointed out as well, while Parthia patch itself up, and focus on culture, science, and trade.
This also could saved the Kushan Empire as they won't have the Sasanians coming to town on them, which in itself would have very interesting affects on the region and on India. (Or at least have someone reunite the western and eastern halves of the Kushan.)