Generally, including is used to get a set of functions or objects into your running script, so that they can be used, although it can also be used as a standalone page or some bit of HTML, like you posted. In reality, it depends on whether you'd rather have another function on the same script or in a remote script, for aesthetics or organization, whatever your reason.
Functions will usually run a bit faster, as server response time and parsing time may make the include function run a bit slower, but for all intents and purposes you wont notice much. Most of the lag will be due to the fact that a local function will be executed with the page, whereas the include function must execute the page, load another page, and then execute that page as well. If that makes sense.