An odd pair with a real question behind it
Nobody replaces a Domo deployment with Julius, or the reverse. The comparison shows up at smaller companies deciding whether to buy a BI platform at all, and at larger ones where an analyst wants a faster scratchpad than the official reporting tool. In both cases the useful question is how much of your analytics is one-off investigation and how much is shared, recurring reporting.
That split decides the answer. Julius is excellent at the first. Domo exists for the second, and its cost and setup only make sense once many people depend on the same governed figures.