The correct response that accurately captures the reactions of the Byzantine and Sasanian Empires to Islamic conquest is:
The Sasanians crumbled due to instability, the Byzantines held out despite losing territory.
This response reflects the historical context where the Sasanian Empire faced significant internal strife and instability that contributed to its rapid decline following the Islamic conquests, while the Byzantine Empire, despite losing substantial territory, was able to maintain its existence for several more centuries, particularly by adapting to the new political realities and managing its resources effectively.