There are competing forces in effect as an operating system like OS X matures and evolves.
1. Tuning. The first version of a product usually has bottlenecks that weren't known in advance. The developer (Apple in this case) can streamline, fine-tune, optimize, rewrite sections of code, or change designs to lessen these bottlenecks. Because of the work involved, these changes are not made globally. They are applied only where there is likely to be a noticable payout from a performance improvement.
2. Bloat. Each new version of an operating system will support new interfaces and standards and add new facilities. For compatibility, old ones are maintained as well. This increases the size of the operating system, making it take more disk space, more time to download and install, and, unless designed carefully, more RAM, even if you aren't using the new features. It can also add to the overhead of performing common tasks.
Effect #1 may make older Macs run faster under Mac OS X 10.3. Effect #2 may make older Macs run slower, or not at all, under Mac OS X 10.3.