Hey Joduffy,
I have done both, with the gameobject and with the script. The options differ between gameobject and script but nothing gives me the option like the one showing in your screenshot, i.e.; Forward running speed property.
I have attached a few screenshots to show what I mean. The first one is with the FPS rigidbody script, the second with the FPS controller game object and the third with the FPS controller script.