For anyone looking for a solution here it is :
You can apply the same smoothing function to your Gamepad GetAxis the same way Unity apply’s it to Keyboard GetAxis
You can read about this here https://answers.unity.com/questions/958683/using-unitys-same-smoothing-from-getaxis-on-arrow.html
//These values are the same values you will find inside Unity > Input Settings
float sensitivity = 3f;
float dead = 0.001f;
//Create another float for the "Raw" GetAxis values
float rawXThrow;
float xThrow;
float rawYThrow;
float yThrow;
void ProcessTranslation()
{
//Get the normal Axis values
rawXThrow = player.GetAxis("Move Horizontal");
rawYThrow = player.GetAxis("Move Vertical");
//Apply the Smoothing function to them
xThrow = Mathf.MoveTowards(xThrow, rawXThrow, sensitivity * Time.deltaTime);
yThrow = Mathf.MoveTowards(yThrow, rawYThrow, sensitivity * Time.deltaTime);
}