So there are a few flaws with the premise here. The first I noticed is the "more mythological than Jesus." I'm not entirely sure whether you are questioning his existence or just the stories of the gospels. If the former, he is near universally accepted by modern scholars, if the later, fair enough, though the broad strokes of his life are mostly accepted.

The bigger, and more relevant to the question itself, is the idea that because something is not written down, it is less valid or less valuable. In the west, we value the written word far above oral or pictoral traditions. However, this is not universally the case. Much of the world, in fact all of it if you go far back enough, has relied principally on oral culture and this oral culture can not only be quite developed, but very reliable and with a long memory. To dismiss evidence because it was principally oral for a long period is a deeply flawed practice.

India during the time of the Buddha had no, or at least extremely scant writing. Writing would remain rare for hundreds of year after him and much of that writing was restricted to the very elite and religious functionaries, as well as some whose jobs it was to read and write for the elite and nobility.

However, this does not mean that they did not keep records or relay stories. Indian religious and scholastic texts were circulated widely with little to no variation in many cases. Despite it being a very oral culture, we have an extensive body of literature dating back thousands of years, some of which has remained very consistent for that. The reason for this is that these texts were taken very seriously and there were people whose "jobs" it was to memorize these texts. These people underwent years, sometimes decades of training to remember a set of texts, being taught it through repetition, memonic devices, and memory training. Not only that, but they were also given the job of recalling them on demand and then training succesors.

It was through this method that Buddhist texts were passed down initially. The "core" canon of texts seem to date back to the Buddha or shortly after, while the majority date to centuries later. Typically, linguists, Buddhologists, and other scholars have determined, or at least speculated on, these texts through a variety of methods; comparing between canons, linguistic analysis, internal comparison, and many more. Through these methods, we can get a broad idea of the age of certain texts.

As for the broader historicity of the Buddha, it is near universally agreed upon. The reason for this is precisely because of the broad agreement of so many canons on the broad strokes of his life, however it was confused and exaggerated over time. For instance, the popular flight from his home was likely from the story of a previous Buddha. However, certain details of his life are quite clear from the texts and seem to paint what outside of the texts seem to be a fairly strange picture for a religious figure. Take for instance the narrative of his death, which is quite ignoble outside of the context of the narrative as he seems to die of some kind of intestinal condition, potentially Messanteric Infraction.

So yes, our info is largely oral, but the core was composed and passed down soon after his death. The narratives are reasonable detailed enough to ascertain things like time period, cause of death, political situation, and cultural values. Actually, the Buddhist texts are generally consider the principal source for the political geography of India at the time and used to assess what the culture and social organization was, coming from a more middle class background than the noble and priestly sources of the Upanisads.