Strictly speaking, I don't think that there is any way to actually split a single book with either tool. That said ...
One method would be to make several copies of the original omnibus ePub, one for each of the individual books and rename them using their new single titles. Then open each, one at a time, in Sigil and:
- Use Sigil's split function to isolate one book if necessary.
- Delete the (x)HTML files that contain the pieces of the other books
- Edit the title page to reflect the new proper title
- Edit the metadata to set the correct title and remove any spurious references to the deleted titles that might exist.
- Regenerate the TOC
- Save.
You'll likely find that step one isn't necessary. Most such omnibuses will contain a number of (x)HTML files and won't have any two book's pieces share a file. Also, you'll probably want to replace the cover image in each to something appropriate. That is easy to do in calibre if you add the Tweak ePub plugin to update the ePub after pasting in a new cover. If you can't find covers you could add the Generate Cover plugin to calibre to generate a cover a bit nicer than calibre's core cover generator.