Unfortunately, while the speed issue would make sense technically, it has not always been true in the past in the actual SmartThings implementation . Sometimes the device handlers which are running locally appear to process more slowly than the ones that run in the cloud.
What local processing will absolutely give you is the ability for smartlighting (the official feature, which is the only smart app which currently runs locally) to operate even if the SmartThings cloud is unavailable.
So if the Internet is out at your house or the cloud itself is down, your local lights can still turn on and off by a local motion sensor.
Please take any additional follow on questions about how local processing works in ST to the following thread, so that we can keep this FAQ just for the list of device type handlers. 