First, the main benefit of ULID is that you can generate the IDs within your own software rather than rely on the database. We can queue them or even reference them before they land in the database. The traditional roundtrip has been eliminated.
Secondly, being able to sort ULIDs is a nice plus, although not that big of a deal. It makes it relatively easy to shard or partition databases, and it provides a convenient sort if you're not looking for extreme accuracy.
ULIDs are also shorter and slightly more user friendly than UUIDs.
In some circumstances we found the actual implementations to be slightly lacking. For example, the JS library for ULID once returned a 25 character string rather than the standard 26 characters, causing a big ruckus that we had to manually resolve.