Character Motor: standard vs. custom ?

Hey everyone,

I'm developing just for fun a "2D pixel runner". Though I had everything clear, one serious problem appeared:

Earlier I asked here how to correctly implement the player movement forward (X axis). Since then I realised that the script below totally overrides the Character Motion script which is attached to the First Person Controller by default.

 MovingScript.js
 
 function Update () {
         var controller : CharacterController = GetComponent(CharacterController);
         controller.SimpleMove(Vector3.right * speed);
 }

There is no acceleration with distance, the player jumps not that high and in general in seems it was working "smoother" before I attached the custom MovingScript.js

A question to the skilled developers with experience: ##Should I use the standard Character Motor and change the moving script or work over all that physics stuff in my own script somehow ?

On this picture the player can jump over the stone cube with (arrows + space bar) and can't with (my moving script + space bar) ###Thank you!