Hi OP! I'm actually a Classical Historian specializing in comparative studies between Rome and China, so let's see if I can explain this somewhat.

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The rise of Roman-Chinese comparative studies is a relatively new phenomenon in history, starting only from the 2000s. This field of study predominantly rose from Graeco-Chinese comparative studies, which started to gain momentum in the 90s. The reasons as for why Rome and China became such a focal point in comparative studies right now are two-fold: why Rome and China specifically, and the rising focus on interdisciplinary studies in general.

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Early Imperial Rome and China actually shared significant similarities, which is all the more fascinating since these two societies - while having indirect contact via the Silk Road and other Eurasian trade networks - never had direct contact during this time period (the first definite contact did not take place until the Byzantine Empire/Tang Dynasty). This makes the two empires ripe for comparisons: on points of similarities (such as their theories on 'race', views on 'barbarians', ideas on 'divine right to rule', etc.), how and why did they develop along such parallel lines? on points of differences, why did they, coming from such a comparable origin, diverge?

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Walter Scheidel, one of the foremost Rome-China comparative historians, asserts that a comparative study ‘defamiliarizes the deceptively familiar’ and, by removing the label of ‘self-evident’, one could explore alternate questions and answers not immediately apparent in mono-cultural analyses. In other words, Roman historians (or mono-cultural historians in general) often erroneously hold that a particular trend or development in the area of their study is 'self-explanatory' or 'inevitable'. By introducing a comparison, we can question whether such a development is truly 'self-explanatory'. For example, Auyang, in her work 'Rome and China Compared', challenges the idea that political rights for 'citizens' was an inevitable and natural progress in ancient societies, by showing that China did not develop what we would consider political or 'citizen' rights until well into the Early Modern age; thus, Rome's development of a complex 'democracy' - I use that term loosely - must have had some unique causes and factors other than 'it was bound to happen'.

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In areas where Rome and China developed along similar lines, we essentially have an additional set of data to analyse a particular phenomenon. Augustus' Res Gestae shared significant parallels with stele inscriptions of the first emperor of China - Qin Shi Huangdi. As such, these two inscriptions can be viewed comparatively, in order to give us a deeper understanding of how these two emperors constructed their imperial image, justified their rule, developed their propaganda, etc. Further topics of exploration can then be extrapolated: WHY did these two emperors construe their propagandist self-images so similarly? Was it because that was what worked? If so, what does that tell us about how humans are swayed by propaganda in general?

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Furthermore, utilizing both Roman and Chinese sources also allows us to understand Eurasia better. For example, both Rome and China had contact with Central Asia and Steppe Nomads - it can never hurt by having another point of reference when studying a culture. Hyun Jin Kim has done significant work regarding this with the Huns and the Xiongnu.

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Here is a short reading list on (scholarly) works in this area:

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Fritz-Heiner Mutschler and Achim Mittag - Conceiving the Empire: China and Rome Compared

Michael Scott - Ancient Worlds: A Global History of Antiquity

Walter Scheidel, et al*. - State Power in Ancient China and Rome*

Walter Scheidel, et al*. - Rome and China: Comparative Perspectives on Ancient World Empires*

Hyun Jin Kim, et al. - Eurasian Empires in Antiquity and the Early Middle Ages: Contact and Exchange between Graeco-Roman World, Inner Asia and China

Hyun Jin Kim. - The Huns, Rome and the Birth of Europe

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If you want to understand the importance and theory of comparative studies a bit more, this is probably the best article on it:

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Hyun Jin Kim. ‘Ancient History and the Classics from a Comparative Perspective: China and the Graeco-Roman World’, Ancient West and East, vol. 14, 2015, pp. 253 – 274.

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Let me know if you have any more questions!