The Greeks (and later the Romans) were a literate society for much, much longer than the Norse. From the writing of the Iliad around 1200 BC to the fall of the western roman empire in 476 that's roughly 1600 years of writing. And that fall isn't even a clean break, the Eastern Roman Empire continued preserving ancient Greek literature until its fall in 1453, and while literate culture dropped off in the west Latin and Greek texts were still preserved in monasteries. So that is a lot of time for myths to be written down (and of course, edited into new forms by playwrights, writers and poets).

You also have to consider the prestige factor that is associated with Greek mythology/literature. For much of the empire, to be considered an educated part of the upper classes, knowledge of the classics was vital. People read the works recording those myths again and again (on top of, of course, oral accounts) because they were the key to high society in the empire. Literary knowledge was basically the equivalent of being a learned person.

This continued into the middle ages. In the former western half there was certainly a gradual decrease in literacy among the elite after the fall of the empire as fighting skills became more important, but these texts were still used to educate monks in Latin and Greek. They preserved the texts and some developed a lot of knowledge of them. When things stabilised again and learning became once again a mark of prestige for the elite, knowledge of classical literature had kept it's position as a sign of knowledge and once again started to be more widely studied. This was helped by the association of this Classical literature with the Roman Empire, an entity which many rulers consciously tried to emulate. And of course, in the Eastern Roman empire, the knowledge of Greek classics as a mark of prestige had never really gone away.

So not only do you get a long "production time" for written accounts of Greek myths, there's also a strong incentive for people to preserve andread them, even after they stop believing in them, both to learn the languages they were written in and more importantly the prestige associated with them.

Then we've got Norse myth. Now, we pretty much have no written accounts of these myths when Norse paganism as a religious tradition was still alive (and of course it was never one uniform tradition so what we have is a very fragmentary reflection of it). The Norse at the time had runes of course, but these were used for short inscriptions, not for the recording of longer texts. It's only with the adoption of christianity that we see a larger literate culture emerge in the region. And there just isn't the same incentive to preserve these myths like there was for classical myths. To put it simply, they weren't fashionable. With the coming of European culture from the south it's bible stories and classical literature that are the things you need to know to seem like a learned individual (although of course, this was a gradual process, as the use of old poems about the gods as entertainment in Iceland shows). So the only records of Norse myths we have are pretty some euhemerised accounts when writers tried to use them to give the Scandinavians an illustrious past or the Poetic Edda from Iceland which was written down to help skalds entertain their noble hosts with the stories, not as a faithful reproduction of a past religion. And this was all in the span of a couple of centuries, as under influence of christianity the old myths were forgotten or refashioned.

So Norse myth simply didn't have anywhere near as many opportunities for recording. Moreover, for Scandinavians newly enthusiastic about Christianity and the European culture it brought with it there was nowhere near as much incentive to preserve it.