I'm afraid I don't have a whole lot of information to offer here, not having worked with Oracle a whole lot. What little I've got, though, I offer.
I haven't seen any benchmarks, nor had the opportunity to perform any useful comparisons, but simply based on the characteristics of the OSes themselves I'd imagine that Linux would be the better performer by far with Oracle. This, of course, is based on a number of largely self-evident factors, such as the lack of a need to support wholly unnecessary GUI environments in Linux, thus freeing up resources for the database itself.
On the other hand, the Linux port of Oracle is relatively new. I don't know how well the port was accomplished. Assuming the guys at Oracle did a halfway decent job, though, Oracle on the Linux platform should leave Oracle on the Windows platform in the dust. You'll have to look into the Oracle port's characteristics, though, to be sure. The most likely place for that sort of information would probably be someone technically knowledgeable at Oracle. This means you'll have to talk to someone other than their sales staff.
Point of interest: Apparently, Oracle controls data management at the filesystem block level. This would explain the high-end scalability of Oracle that is so vaunted in the industry, of course, because by managing data at that level directly, a lot of wasted time in disk churning on the server is cut out. Seek times wouldn't be shortened any, of course, but the translation of a request for data (for instance) from DBMS activity to drive access would be streamlined drastically.
The downside comes up with filesystems that don't use blocks. Sector-based filesystem management, for instance, would be problematic for Oracle. A real-world example of the incompatibilities involved would be ReiserFS. This filesystem doesn't manage data at the block-level. Because it doesn't limit itself to data management in segments no smaller than blocks, ReiserFS makes far more efficient use of storage capacity when dealing with small files, but this also makes it incompatible with Oracle, it seems. Thus, when setting up Linux database servers for use with Oracle, make sure you choose the right filesystem. Ext3 should work fine, and (like ReiserFS) is a journaling filesystem.
