There's no reason you can't use a mouse a velocity input and a stick as a position input; either one is returning a value in a two-dimensional space -- treating that value as "position" or "velocity" is a matter of what the receiving software does with the input, not the input itself.
Joystick calibration utilities, for instance, tend to take stick position as a position input, and ISTR a number of PC sims that preferred joystick input but could use a mouse like a non-auto-centering joystick.
> That is hardly relevant, using a stick as position input would give you, what, five units of movement on either axis?
From what I can find online, the PS3 controller is 10-bit per axis (1024 positions on either axis), the Xbox 360 is either 8-bit (256 positions) or 16-bit (64k positions.)
A 25-way joystick of the type you describe wouldn't be usable for most console games, whether as a position or velocity input.
Joystick calibration utilities, for instance, tend to take stick position as a position input, and ISTR a number of PC sims that preferred joystick input but could use a mouse like a non-auto-centering joystick.