I didn't vote because my option isn't there. I'd split some, but don't have the tech knowledge to do so.
In general, I have no need to split an omnibus of books unless there is no table of contents. I list the books individually in my Goodreads account, so storing or reading as an omnibus is not an issue. I'd like to be able to split anthologies, so that I could keep novellas and short stories of specific authors together with their series, but don't know how to use the software to do it.
Be aware that some omnibus editions are not complete. The only one I know specifically is the Dragonrider's of Pern Omnibus (1st 3 books) by Anne McCaffrey because this omnibus was geared towards the YA market. Some scenes in the original were dropped as inappropriate for this market. However, this problem was present in the paper version, not deliberate towards ereaders.