Run this as admin in both the database where you have trouble and and one there is working.
EXECUTE AS USER = 'abamgr'
go
SELECT * FROM sys.user_token
go
REVERT
go
SELECT r.name
FROM sys.database_principals r
JOIN sys.database_role_members rm ON r.principal_id = rm.role_principal_id
JOIN sys.database_principals u ON u.principal_id = rm.member_principal_id
WHERE u.name = 'abamgr'
go
SELECT *
FROM sys.database_permissions dp
JOIN sys.database_principals u ON u.principal_id = dp.grantee_principal_id
WHERE u.name = 'abamgr'
Replace "abamgr" with the name of your non-admin user.
Compare what is different between the databases. If there are no direct differences, then you may have to look at roles or Windows groups the user is a member of
It is not practical for us to use the Installation Center for the upgrade. We are calling "SETUP.EXE" with a configuration.ini file to do the install. Can I just modify the configuration.ini to do the upgrade? I'm assuming at least the Action value should be updated.
It appears that the /ACTION switch also accepts the option UPGRADE, although the documentation says otherwise. (Myself, I don't install SQL Server that often that I bother about using the command line, but I'm content with using the wizard.)