Been listening through Mike Duncan's The History of Rome podcast, and he seems to believe that Jovian could've fought it out, as Shapur II was reluctant to fight the Romans, even while weakened from harassment and Shapur's scorched earth tactics.
Is there enough knowledge about the strength and condition of both sides to know if it was worth it to try to win?
Bonus question: Duncan speculates that had they fought it out, that it would've not led to the issues in the East that would continue for years to come, with the Sassanids being emboldened and the Romans bitter and vengeful. Any comments on this as well?
As of Julian's death, the Roman army in Persia was in a precarious situation. While there was a reinforcement army under a certain Procopius waiting (originally meant to reinforce Julian), it was not in communication with Jovian's army. The supply lines on the Euphrates had been burned, and the Sassanids had flooded or otherwise destroyed fields so Romans couldn't forage from them. Immediately, there were problems of supply. Also, the Sassanid army was nearby but refusing to engage, instead harassing the Romans with occasional cavalry attacks.
Shapur II's strategy of not fighting the Romans was a sound one- it's always been controversial whether the Sassanids composed a full-blown rival superpower, and Romans still regarded themselves as superior to the Sassanids and other "barbarians." By harassing the Romans and cutting off any sources of supply, all the Sassanids have to do is keep the Romans from getting out. Tactically, the Roman army was still very powerful. Thus, not engaging makes sense to avoid heavy losses. The Roman army was getting weaker by day. Sassanids had not taken any losses. By the time Julian was dead, a Roman victory was very unlikely- certainly not before another Roman invasion could be organized. As a larger strategy, the Romans cutting their losses, getting out, and trying again later was probably the best one available at that moment.
However, even if the Romans had won, conflict would've likely continued. Romans had won wars with the Sassanids in the past. They'd even taken Ctesiphon under Diocletian. Both the Romans and the Sassanids regularly disagreed both about their borders in Mesopotamia and who should dominate Armenia. That said, in actual history, while there were a couple of major conflicts between the Romans and the Sassanids in the next few decades, the 5th century was relatively quiet, with only one major war. Because both the Sassanids and the Romans were distracted by other invaders, it's not likely that a different outcome to the war in 363AD would've changed this.