I personally like the subpixel one you made, it gives a fairly strong sense of form. However, the reason why it looks like a flashlight passing over it is because you shifted only the lights. From what I understand, shifting the details inside the form is just as important as shifting the lights.
With the more bouncy version, it's odd that the centre part doesn't move very much. It's dissonant between the cartoony extreme movement of the wheels and the realistic movement of the subpixel one.
Some things to consider:
Shifting the tread shadow makes it look like the treads are growing in size vertically, doesn't work well.
You might want to give up on the jumping around entirely, instead having the treads and the engine pipes move. If you still want to have that, then I feel you'll probably have to shift the middle part too. It's solidly connected to the base, after all, and there are no springs to make it a smoother ride from what I know.