The main purpose of PC connections is to fire, via a wired connection, studio flash units not mounted directly to the camera. The only signal a PC connection carries is that the shutter has opened and the flash should fire. It is not capable of carrying any other data. As the capabilities of wireless triggering methods have increased, wired connections of any kind between camera and external flash units not mounted on the camera are waning in popularity. Many newer camera models don't even include a PC connection in the design. If a photographer needs to signal external flash units via PC connection, then an adapter attached to the camera's hot shoe can accomplish this.
The hot shoes of most current cameras, though, are capable of communicating much more data beyond a single triggering signal to a compatible flash. Canon's E-TTL system, Nikon's i-TTL system, as well as the systems of other manufacturers use multiple contacts on the hot shoe to communicate in both directions between the camera and flash unit. This allows things such as automatic flash metering, power adjustment, second curtain sync, and controlling multiple flashes via optical pulses between the hot shoe mounted 'master' flash and several external 'slave' flash units.
If a photographer desires a wired TTL connection off camera, hot shoe cables that include wires for all of the connections between the hot shoe and speedlight are available. Wireless triggers can also attach to a hot shoe. Some wireless units only transmit a single signal, like the old PC connection, that tells the flash to fire. Others allow the full communication between a camera and flash that enable the same functionality as if the flash where mounted directly on the camera's hot shoe.
Which of these connections will work best for you depends on what flash units you have, what camera model you are using, what amount of communication you need between the camera and flash, and how much your budget is.