I don't have practical experience with JIRA Cloud Operations, or JIRA on-prem operations, but if I compare on-prem vs SaaS of our own solutions, the answer is scale and focus.
If I combine our three internal ticketing systems, we end up with something like 200k - 300k tickets, with maybe up to 5M comments on those in JIRA-Terms. If you throw a small-ish, decently configured postgres with 8GB - 16GB of memory at it, it'll keep most to all of that in memory at all times, indexes will be analyzed and fine-tuned to your specific dataset. It will answer queries very, very fast. Any cache in the application servers will also be primed with your data 24/7, speeding it up even further.
JIRA Cloud is most likely not an in-memory problem as a whole at a database layer, so it is at quite the disadvantage performance wise for a small customer.
(In case this turns into a SaaS-Hate-Thread: Yes our customers could have a faster system if they were on-prem. If they had the same experience and expertise running postgres as well as all the other necessary middlewares. And then we're not talking about non-functional operational requirements such as availability, emergency scalability or backups yet)
My guess is that self-hosted versions have an infinitely simpler user experience when it comes to accounts and visibility. Jira Cloud is definitely angled towards always being behind some sort of an account system, which used a real, costly backend, but the self-hosted one can get by with the local hosted IdP or an LDAP server.