Note that I'm speaking here of my preference strictly for Oracle-hosting purposes, and that everything I say about "Linux" really applies to all POSIX-based systems (like Solaris, which I started on as a DBA).
I've used Oracle on Windows and Linux for many years, and on Solaris many years ago. I prefer Linux because:
1. Oracle releases patches, new versions, and sometimes security updates for Linux significantly before they are available for Windows - there's usually about a two month lag for Windows (one month for Critical Patch Updates).
2. Our Windows servers have crashed or locked up occasionally, and very frequently require reboots for patch installation. Oracle itself stays up very nicely, but Oracle can't keep running on a machine that is down. This hasn't been a problem for me on Linux.
3. Oracle's interaction with Vista's User Access Control is a nightmare. I'm constantly finding that the dedicated Oracle user account, which was used to install Oracle, nonetheless lacks permission to edit or even see Oracle-generated files - like newly generated logfiles. It could be that I'm making some mistake, but permissions shouldn't be confusing; and on Linux, they aren't. (Most servers don't run Vista, but I'm afraid of what this forebodes for future versions of Windows Server.)
4. Thanks to the Windows Registry, cleanly removing an installation of Oracle from Windows is tricky and tedious. The Oracle Installer has gotten better at this since version 10g, though.
5. Better tools. Linux find is infinitely better than any native Windows search tool. It can take you minutes on Windows to track down what Linux which tells you in an instant. Also, Oracle uses and generates plenty of plain-text files, and Linux comes with better tools for handling text files - good text editors (unlike Notepad), shell commands like head, tail, grep, etc. You can try to catch Windows up by installing Geanie, Cygwin, Google Desktop, etc. on a Windows machine, but it's better not to have to (especially since Cygwin installation is not completely newbie-friendly).
I can only think of two Windows advantages over Linux:
1. In Oracle's command-line tools like sqlplus, rman, etc., you can scroll through and re-run past commands using the up- and down- arrow keys - but only on Windows. You can fix this on Linux by installing rlwrap and always invoking the Oracle tools under rlwrap:
rlwrap sqlplus me@myinstance
2. Quest's TOAD is only available for Windows, and it is an infamously useful tool. It doesn't need to be on the database server, though, just on a machine that can connect to the database. Also, Oracle's free sqldeveloper is one among several viable alternatives; it will probably never catch up to TOAD completely, but it's good for the bulk of what most people use TOAD for.
In general, however, I should emphasis that Oracle's ancient boast of running on everything really is true. As a DBA, I prefer Linux for the reasons listed above, but to my database users, it's absolutely irrelevant (downtime aside). I could move my production databases to a different OS overnight, and tomorrow, my users would have no idea that there had been a change.