Hi Scott,
You can tell really easily if its business edition. As a BE server has both CUCM and Unity connection hosted on the same server. When you point your ip address to the CUCM in the web browser, just put in the ip address and not full url like https://x.x.x.x/ccmadmin just https://x.x.x.x if its BE, under installed applications you will see two options:
Cisco Unified Communications Manager
Cisco Unity Connection
Also even if you are logged into the CUCM admin webpage, from top right navigation pane, you will see, in addition to all CUCM options like Serviceability, CUCM OS admin etc., all options for Ciso unity connection as well like Cisco Unity Connection admin, servicability etc. Both options together will only show up if its a BE server, not for a CUCM or CUC only deployment.
In the end if you want to find out the exact model, i think you can check either from the cli by running show hardware or OS admin page by visting show hardware.
Hope its helpful.
Terry