It would be easier, I guess, but would it be worth it? Justinian pushed the Persians back far to the east, reconquering Mesopotamia, expanding Roman control of the Caucasus, and even he took bits of Western Persia itself (though they would lose that bit). Going west would be pretty bad anyway, even if it would be somewhat easier. The Ostrogoths would be defeated, but Italy would be damaged as well. Not sure whether the East or Italy would've been more profitable, but I'm going to say Mesopotamia would be more valuable. Justinian's complete destruction of Persian power also ensured they would remain weakened for a long time, as Persia fell into a massive civil war. This probably saved the Byzantines from the Great Arab Invasion, which was a narrow victory OTL. Without Persia being defeated, they would've backstabbed Rome while they were defending against the Arabs, which would weaken the Empire so badly it basically would end up losing the West anyway.
So going west we probably see Persia pushing deep into Anatolia, and the Arabs conquering the Levant and Egypt would fall to someone. The West would obviously end up falling as well, with Italy probably being invaded by the Pope or the Franks or any other kingdom around there. The Byzantines probably don't survive until the modern era as they have IOTL.