Should I use two databases or two schemas?
When using one database with two schemas you also share SGA structures(like library cache) and also possibly TEMP tablespace and also backups. In rare cases one application can have negative impact on other's performance. Also if you are asked to revert one schema it will be much harder to "restore" just one schema. The same also applies to patching, it's harder to request a downtime from two different customers.

If you use two schemas then definitely create separate DATA and TEMP tablespaces. (You can not have separate UNDO).

If you use two databases then you can not share RAM between them - for buffer cache. You can partially bypass this limitation by using OS level buffer cache. Simply disable direct file access. 
A separate database can also be easily migrated onto another machine using RMAN or simple pure scp/rsync.