Are there any doctrinal differences between the Nishi Honganji and Higashi Honganji branches of Jōdo Shinshū?
Simple answer, no.
There are more than 10 branches of Shin Buddhism— the largest are Jodo Shinshu Hongwanji-ha (aka Nishi Hongwanji) and Shinshu Ohtani-ha (aka Higashi Hongwanji).
They split in 1603, as both a political ploy by the new shogun (Tokugawa, Ieyasu) and by a family feud between brothers as who should be the monshu (abbot).
By doctrine, there is no difference in that the lineage of Shinran and monshus (including Rennyo, the great reformer and organizer) remained the same.
Since that time, there have been efforts to show the superiority of one branch or the other, and subtle changes, like the title of things chanted. For example, Nishi Honganji uses San Butsu Ge, and Higashi Honganji uses Tan Butsu Ge—the same words with just a different pronunciation.
In more recent times, say since the Meiji Restoration in 1868, the modernization of Japan has also created some subtle differences. First, Ryukoku University (Nishi) and Ohtani University (Higashi) have been in academic competition.
And maybe in the last 50 years, there have been more subtle differences in what part of the doctrine is emphasized.
Gassho (with palms together), Rev. Ron