Lots of dependencies.
For ex, if you upgrade your EBS database, then automatically OBIEE database will be upgraded too.
The new Oracle DB version may be certified by EBS , but not certified with OBIEE.
Any bugs which may be triggered by OBIEE RCU Sqls, will affect the EBS database and thus EBS applications.
When you do some ops on EBS database, OBIEE will be affected too. Planned downtime for EBS database will be a required downtime for OBIEE as welll.. and vice versa.
Any performance problems triggered by queries on OBIEE schemas , will affect the EBS database performance and vice versa..
Licensing will be complex.. Some day, Oracle may complain and say that you are using EBS database for other purposes..