Each has its own advantages.
Hot shoe, as Dan pointed out, facilitates a two-way communication between camera and flash and allows TTL and its variants to work. This is designed to give accurate flash exposures without having to manually figure out your flash settings - just set the flash to TTL and away you go. The disadvantage here is that because the flash is mounted directly on the camera, you will typically get harsh shadows being cast just behind your subject.
There are hot-shoe extension cables available for some cameras that allow the flash to be mounted off camera (typically to one side or the other) and still maintain the TTL communication. These cables are not usually very long.
PC Sync is just a simple trigger cable with no TTL functionality. Therefore you will have to either use a flash meter to obtain flash output settings or think "Ok, I'm about this far from my subject, my aperture is f8 and my ISO is 100" and set your flash manually. The advantage is that sync cables are usually longer than a hot shoe extension cable and you can move the flash further away from the camera and control your lighting a little more.
So, you see it's really a matter of how you want to use flash, the subject etc that may make one better than the other. Personally, I use E-TTL hot shoe extension or IR controllers as I hardly ever use the flash on camera. Besides my camera doesn't have PC Sync :). Sorry, a bit long winded there. I think you will find the PC Sync is a dying breed for most although there is probably still a good use for it in a pro studio.