The correct answer is: Both empires controlled Asia Minor and the Italian Peninsula.
Reasoning: Both the Byzantine Empire under Justinian I and the Roman Empire under Trajan had significant control over Asia Minor (modern-day Turkey) and the Italian Peninsula (which includes Rome). Asia Minor was crucial for both empires as a strategic region for trade and military purposes, while the Italian Peninsula was the heart of the Roman Empire, a central area for both governance and culture. The other options do not accurately represent similarities in territorial control between the two empires.