I've recently begun reading Kalevipoeg and The Kalevala, but I've begun reading about them as well. I'm aware that they were written in the 19th century, each by a single man (Lönnrot and Kreutzwald) who based their respective stories on folk tales they collected from their regions. So how is it that they managed to create true "epics" out of scattered stories? It seems more likely to me that they based their epics on tales they collected, then filled in the gaps to form a cohesive narrative. But how much, exactly, did they add, and how much was "authentic?" Were they more Tolkien, or more Homer? Were Lönnrot and Kreutzwald even similar to each other? Did one base their work more on authentic folk tales than the other?
This is a great question. I think we would have to say more Homer than Tolkien. They are in the tradition of the Brothers Grimm, but also of Robert Burns and his "Musical Museum." The Romantic-era interest in folk literature, particularly of people who sought to solidify their ethnic identity in the face of more powerful neighbors, inspired people of the period to collect and publish this material. In each of these cases, there was a certain amount of "improvement" inflicted on the folk material, changes that do not meet modern standards of folklore collecting.
At the same time, there had always been a literary tradition of drawing on folk motifs to write stories that seem like they were composed and transmitted by the folk, but were in fact artistic fabrications - at least for the most part. Wilhelm Grimm was particularly interested in this genre (Jacob much less so). And Burns wrote lyrics to folk tunes, or applied old folk poetry to existing folk tunes, even if the two were not originally connected. Hans Christian Andersen is squarely in this camp, writing stories that seem like folktales, but were of his own invention. And so is Tolkien. But this type of literary tradition is separate from the Finnish Kalevala and the Estonian Kalevipoeg, which are more completely rooted in and fairly faithful to the folk tradition.
A good source for this is Lauri Honko, (1990). Religion, myth, and folklore in the world's epics: the Kalevala and its predecessors. His work is a classic; but many Scandinavian folklorists wrote about and were intrigued and inspired by these publications.
edit: a small point, but these are folk ballads, drawing on an indigenous folk-style of poetry and singing of legendary material. And by legendary material, I mean that they were taken by pre-Christian believers (and many after conversion) to depict events that really happened, as opposed to folktales, which were fictional - an oral form of folk novels.