I think the main problem is the lack of structure in the original concept. It's all flat shapes. Without strongly defining the volumes first it is not possible to imagine light and shadow accurately.
In your pixel version you are implying some volume by the lighter and darker areas but it does not appear to match up with the contours.
To fix that, make a stronger concept first. Draw a side view, a front view (and maybe even top and bottom views) and after that make a construction for the pose you want to render. That should help you work out the volumes before you try to illuminate them and will lead to a much more defined and more coherent result. Don't cheat, don't wing it. Designing the different views first and going through that whole process will give you a better understanding and insight into what you're trying to render afterwards.