The current docs we have in regards to JIRA using Oracle database do not go into the different editions offered by Oracle.

However the Express edition has limitations in regards to the size of the database itself, as well as the system resources that can be allocated to it.

Oracle Database XE can be installed on any size machine with any number of CPUs, stores up to 4GB of user data, using up to 1GB of memory, and using only one CPU on the host machine.

Oracle Database Editions has more details.

Because of this limitation our products like JIRA and Confluence can reach these limitations in large customer environments and cause performance limitations within our products because of this. I expect this was the same logic in regards to why the MS SQL Express editions are also not listed on the supported platforms. They have very similar limitations in regards to how large the database can be, and I think there is a 1GB memory limitation there as well.

Requesting to update the JIRA supported platforms docs to reflect that we should not be supporting environments using the express editions.
JIRA 7.3 Supported platforms - Atlassian Documentation