Final answer:
Both Ibn Khaldun, with his foundational work on historical sociology, and Ibn Sina, with his extensive contributions to philosophy and medicine, brought profound and distinct impacts to the Islamic Empire and beyond. The significance of their contributions makes it inappropriate to rank one as more impactful than the other.
Step-by-step explanation:
When comparing the contributions of Ibn Khaldun and Ibn Sina to the Islamic Empire, it is clear both individuals had significant and rather distinct impacts on their respective fields and thus on the civilization as a whole. Ibn Khaldun is notably recognized for his pioneering work in the field of historical sociology. He provided foundational insights on social dynamics, the rise and fall of empires, and the concept of asabiyyah, or social cohesion, especially in his work the Muqaddimah. His studies have informed not only the historical understanding of Islamic societies but also modern sociology and economics.
Ibn Sina, on the other hand, was a polymath whose contributions spanned multiple fields, most notably philosophy and medicine. His Canon of Medicine was a standard medical text in Europe for centuries, reflecting the far-reaching impact of his work in medicine. Additionally, his thoughts on rational order and empiricism influenced both Islamic and European thought, bridging the gap between classical Greek philosophies and later innovative approaches in both the Islamic and Western worlds.
In conclusion, attempting to deem one of these figures as having a 'more significant' impact on the Islamic Empire diminishes the distinct and profound contributions each has made to history and human knowledge. Therefore, it is more appropriate to state that Ibn Khaldun and Ibn Sina both contributed uniquely and significantly to their Time and legacy.