Unless you're new here, you've heard of PostGIS several times. It's really hard to find documentation about spatial database benchmarks since, if I'm not mistaken, proprietary software licenses often prohibit publicly sharing such benchmarks (am I right?). And I guess there's at least one good reason for this: doing fair benchmarking is difficult to accomplish. But here's one (currently available) benchmarking report comparing PostGIS (PostgreSQL) and Oracle Spatial.
From the conclusions of the 46-pages report: "From the experimental results that we saw, we can conclude that Postgres performs better than Oracle 11g both in the Cold Phase and Warm Phase. Though in few queries Oracle 11g performed better but on the whole Postgres overpowered Oracle 11g. In the warm phase in 3 out of 4 queries Postgres performed significantly well, from this we can conclude that Postgres has better automatic memory management capabilities and page replacement policies. [...] Since Postgres uses the underlying GEOS (Geometry Engine - Open Source) library functions for implementing the geometric operations whereas Oracle 11g implements them on its own, and since in majority Postgres performs well, we can conclude that GEOS geometric algorithms are more efficiently designed than Oracle 11g. And also Postgres planner is more efficiently designed to take advantage of any available indexes to use in queries for achieving better performance whereas in Oracle 11g we saw that we have to specify them explicitly through functions."
Here's what Paul Ramsey of the PostGIS fame has to say about it: "Methodologically there are two obvious issues: one is that the Oracle database was on Windows while the PostGIS database was on Linux; the other is that neither database got any tuning, they were both installed and run with default parameters. However, this is one of the nicer comparisons I have read: concise, focussed and with enough technical detail to evaluate what's going on."