I use Oracle 8.1.7 with Analysis Services. I can't really compare between the performance with SQL Server, but performance is OK with Oracle. We use views as the sources, so those needed to be tuned.
The processing of a cube gives you the exact SQL statement it performs, so you can tune these. These will eat up considerable space in the Oracle temp tablespace, because of the sorts.
Another factor is of course the network speed between the database server and the Analysis Services server.
BTW: Because we encountered 'Data Source errors' we now use (after some hours searching for a solution) the Oracle provided OLE DB provider for defining the cubes and dimensions and the 'Microsoft OLE DB provider for Oracle' for processing those. Don't ask me what the difference exactly is, but this way it works fine for me.