In Pure Heart: Ninjutsu Chronicle fictional series, the Momochi and Fujibayashi are rival groups. The rivalry between two jonin policies play a wide role within the series.
There are very few sources, possibly as rumors, but the Momochi clans and the Fujibayashi clans were apparently fierce rivals with one another. Since various families wanted to exert control, especially from the central government, Iga Province was a dangerous place to travel. The in-fighting, especially among the samurai daimyo, provided the shinobi families an opportunity to hone their skills and sell them. The reigning Hattori Family served the Tokugawa like true vassals, while other families were watari ninja (渡り忍) and hired by the daimyo lords because they bid the highest or had advantageous goals.
For Seishin, Fujibayashi and Momochi fight with the province's best interest in mind, believing that they could rule with a strength on par with the Hattori Family. Momochi is more of an "independent faction", and the leader wishes for Iga Province to only serve a freelancer nation that is available to hire. On the other hand, Fujibayashi is a loyalist on the side of Hattori. It is said that he has the blood of the Ashikaga within him, giving him flexibility and connections to the stronger daimyo. Ultimately, choices depend on the Iga Sokoku Ikki.