integration - Moving sprites using the accelerometer (Android)

In my previous game, I was moving my sprite like so:

float time = 10f;  //Number of seconds to pass a pre-defined area (using the screen width in this example)
float velocity = 1f/time; //work out velocity based on above time

float realX-=velocity*dt; //Move the sprite to the left (where dt is previously defined delta)
x = realX*screenWidth //convert to screen coordinates so it can be rendered

sprite.draw(x, y); //Working out the y position in the same way

This all works great when using touch controls. In the above example, the sprite will cross the screen in precisely 10 seconds regardless of the device on which it is running.

However, the game I'm currently developing uses the accelerometer to move the sprite. (I'm only moving the sprite left/right). Currently, what I'm doing is this:

@Override
public void onSensorChanged(SensorEvent event){ 
    tilt = event.values(axis);       

}

Once I have the value, I apply it to my sprite movement like this:

float time = 10f;  //Number of seconds to pass a pre-defined area (using the screen width in this example)
float velocity = 1f/time; //work out velocity based on above time
float realX-=(tilt * velocity)*dt; //Move the sprite to the left **Now using the tilt value*
x = realX*screenWidth //convert to screen coordinates so it can be rendered

Although this does work - it gives nice fluid movement of the sprite, when I run it on an old Galaxy Ace, the sprite accelerates way too fast. This changes the feel of the game - note I'm talking only about acceleration here, so if I tilt the phone from left to right repeatedly, the sprite is extremely (too) responsive on the Ace, but 'just right' on my 10" tablet).

I've tried a couple of other available games and they seem to run pretty consistently across devices.

I'm wondering if my code is correct and if so, what can I do to get all devices running more consistently with regards to the accelerometer?

Edit

Just to clarify what it is I'm asking. I have a sprite in the middle of the screen sitting on a horizontal platform. When the device is tilted to the left, the sprite moves to the left. The rate of movement should be linked to the angle the device is tilted. So, if the device is vertical there should be no movement. If the device is tilted slowly to the left, further and further the sprite should increase in speed also (up to a limit) ie, accelerate.

The other (real world) way to think of it is sitting a ball bearing inside a vertical box (the box representing the device) and then simply tilting the box to the left and right. The ball accelerates towards to lowest corner. The sprite should act like a real ball. If it's accelerating towards to left corner, and the box is tilted in the opposite direction, then the sprite should start to decelerate to a stop, and then srart accelerating in the opposite direction. Just as the real-world ball bearing would.

My Original code achieves this, however, on some devices it's simply too responsive, it will decelerate and accelerate too quickly. And therefore change the 'feel' of the game - making it too easy for one thing.

So basically when I say the sprite movement feels 'natural' I'm referring to how the ball bearing would act/feel in the real-world.

This is exactly what I'm looking for - hope this helps!