I've honestly never used Oracle spatial stuff directly, and begin a huge fan of PostGIS, I've never felt the need to. However based on talking to people I've worked with, at least a few years ago, Oracle was better when dealing with huge amounts of data.
That being said, PostGIS seems far more popular among practitioners from what I've seen. And it's quite common for the first step in any new GIS project to be to copy the relevant subset of data you're interested in from the Oracle database into a PostGIS database and then use that.
The FAA gave a talk a few years ago about how they moved from Oracle spatial (if I remember correctly) to Postgres/PostGIS for cost reasons, and it turned out to be significantly better all around.
Some links (couldn't find a good primary source): https://twitter.com/magnushagander/status/11107130700 http://scanningpages.wordpress.com/2010/04/11/pg-east-2010-2...