Theodosius set up his eldest son, Arcadius, as the Eastern Emperor, and his younger son, Honorius, as the Western Emperor in 395.
There was some sense in putting the elder son in the East, but it wasn't an automatic decision. Constantine the Great did basically the opposite, and Valentinian took the West for himself and set up his brother in the East. The two halves seem to have roughly equal population, and while the East had more trade and a stronger cash economy, the West seems to have been stronger in agriculture and had a stronger military.
One detail that would make a big difference is whether Illyricum would follow Arcadius to the West, where it had been attached in previous divisions, or if it was attached to the East IOTL. My guess is the former.
This supposes that the advisors of Arcadius and Honorius are also switched, namely Stilicho winds up with Honorius in Constantinople. As both boys were too young to rule, there is not much divergence if this doesn't happen.