It might be tempting for someone to look at the raw numbers of the military for both empires to see which was more powerful, but it's very important to remember that most of those forces would already be engaged on one frontier or another, since the cost of maintaining an army wasn't worth it unless they had an immediate responsibility of keeping the peace.

With the mindset I described above, it's confusing to many people how such a great power as Rome could fall in the west to barbarians when the largest invading army up to Attila was only 30,000 strong (Alaric's combined Gothic forces) with most in the range of 10-15,000 when Rome's total military in the late empire is estimated to be between 300-400,000. The fall is due to the fact that there were very few reinforcements to be drawn from other frontiers without the whole thing collapsing completely. Even in times of peace, the Eastern Empire needed to keep roughly 40% of all its armed forces stationed near Sassanid Persia, and in all situations where the Sassanids and barbarians beyond the Danube attacked simultaneously, the Romans would always prioritize their response to the Sassanids. Which is great for the East, because any invading army in the Balkans would be bottled up there and unable to disturb their economic powerhouses of Syria and Egypt. The West wasn't so lucky, because an anemic border defense along the Danube meant that the invaders could waltz right over to Italy, Gaul, and Spain to compound any pressures already felt along the Rhine. Couple this system with the complete lack of any official means of passing on the job of Emperor means that there can be invasions in the heart of the West with a paralyzed imperial center unable to form a coherent response.

I can't really answer your question definitively, because that's better suited to /r/historicalwhatif, but I hope this has given you more insight as to how it's more complicated than raw numbers.