The correct statement that identifies a similarity between the territories controlled by the Byzantine Empire under Justinian I and the Roman Empire under Trajan is:
Both empires controlled Asia Minor and the Italian Peninsula.
Reason: Both empires had significant influence and territorial control over Asia Minor (modern-day Turkey) and the Italian Peninsula (including Rome), which were key regions in both the Byzantine and Roman Empires. The other statements either incorrectly suggest that both empires controlled regions they did not fully occupy or assert claims that lack evidence based on historical accounts.