Too many barbarians coming from the Eurasian Steppe which make the long term stability of Rome and Persia difficult at best. And then consider the barbarians from the southern fringe, the Berbers and the Arabs.
Persia is definitely more exposed to outside threats, though, plus also has the problem of strong Indian states emerging to seize their wealthy territory around the Indus. This might be even more of a problem as the Viking Age is for Rome, or in general the effects of the heavy plow in Northern Europe which allowed for more complex states in the region meaning potential threats to Rome.
Basically, we can expect several quite brutal periods of fragmentation in both states over the centuries, much like China (or Persia).
Ignoring the pink bits and the Roman colonies in West Africa, which are implausible, I would give both Cyrenaica and the Aegean Coast to Rome.
Persia would definitely have the upper hand, though.
Strategically, it's easier to defend Cyrenaica from Egypt than it is from Carthage/Tripolitania, thanks to the Gulf of Syrte's difficult navigation conditions and the fact the region between Tripolitania and Cyrenaica's population centers was sparsely populated and poorly watered.
I don't see why Roman colonies in West Africa would be so implausible, although I think they're in the wrong place. Dakar or Saint-Louis is probably better than Gambia or Casamance. The New World colonies are rather implausible, though, as is the fact Rome does not control the rest of Mauretania.