Although things are definitely more granular if you ask a question that, in effect, touches upon several thousand years of history, I think the primary difference is mostly the following:

The Chinese emperor (Chinese studies are not my field, so correct any inaccuracies) was more or less “merely” the mediator between the divine will and the world of men, but in theory, anyone could ascend to this position. Hence, if his reign was no longer reflective of this higher will, i.e. became depraved, a revolution and dynastic change was legitimate.

The Japanese emperor was, on the other hand, allegedly descended from the deity Amaterasu ōmikami, and therefore the notion of direct lineage (i.e., bloodline) became intrinsically related to the qualification for emperorship. He was located at the center of the symbolic field created by the imperial court, which relocated the original patrimonial imperial household administration within an institutional framework adapted from the polity of the Chinese T’ang period.

Unsurprisingly, the typically explanation is that ideas like regency governance (under the Fujiwara), insei rule (governance by the retired emperor who was the linear ascendant of the reigning emperor), and the emergence of a second political center focused on a supreme warrior leader (shogunate government) instead of replacing the imperial family outright are precisely because of this genealogical requirement and the power relationships that subsequently developed between the ruling elites.

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(edit: Also, keep in mind that in Japan, the court bureaucracy, despite adapting Chinese institutions, remained a hereditary elite which restricted access to specific rank and office to a limited selection of people. This concept of aristocracy had been long-abandoned in China's imperial administration, which introduces a very different environment that the respective ideas of imperial authority had to interact with. In other words, in Japan you could replace a minister with his brother or son, but not with a completely unrelated person. At least in theory, this gives a sovereign a theoretically higher potential to dominate the polity vis á vis his surrounding elites.)

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It is possible to go into more detail, but such a general question could result in writing a whole book (or two).

So, to give one general example: what the Japanese emperor actually did (or could do) at any point in time would require a study of the code of laws and social practices at the respective time, which did change greatly—with the introduction of the first codes of law and established of T’ang style bureaucracy, for example, checks and balances were introduced which involved pretty much the whole stratum of court elites in the political decision-making process and restricted the theoretically absolute power of the emperor, who even was subject of some laws which in practice restricted his limitless authority (which manifested itself especially the drafting and promulgation of the majority of imperial edicts, although there were exceptions). But, yes, he did more than just perform some important rites at new-years, since even later on, he was able to promulgate certain edicts, had to sign others, and so on 😊

I think the bigger issue with the “symbolic” position one might be tempted to associate the emperor with is that eventually, a lot of the time, the reigning emperor was just a child, overshadowed by his father or grandfather, who in the 11th century became the de facto ruler. However, in general, the authority that a single individual could exercise is always also greatly influenced by the specific balance of power between the various historical actors at any given point in time. (Suffice it to say, this is valid for virtually any autocracy in history.) For example, Emperor Godaigo in the late 13th, early 14th century in Japan was a very influential and powerful emperor who had a great part in the destruction of the Kamakura shogunate and indeed did rule directly—albeit only for a few years.

Hope this helps for starters :)

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P.S.: Anyone commenting on the Chinese side of things would be appreciated :)