Like all good security questions, the answer to this one is "depends".

In terms of reliability, it's generally safe to say that hardware is more reliable than software, so if that's your priority, a decent hardware router is your best bet. Even a Linksys can be quite stable if you use the most recent firmware.

Another consideration is exploits. PCs, being more complex than routers, have more potential and practical exploits. With a router, you'll need to make sure you've got the most recent firmware, but with a PC, you'll need to make sure every service it's running is patched fully.

Lastly, I think it's worth pointing out that PCs. especially old-ish ones, use VASTLY more electricity than a small router. While this may not seem like a big deal, remember that this is something that'll be on all the time for the forseeable future. The difference can add up to some serious cash.

If you're really into fine-tuning your firewalls and access lists and stuff, I recommend the WRT54G, which has many excellent third-party firmwares, and the ability to run a linux kernel.