The main problem with the bottom one is that it has a bad case of the jaggies, mostly. In addition to that, it doesn't seem to have much correct anatomy to it. (yes, there is more than that wrong with it, but let's start with small steps to improve upon it)
Stupid quick reference:

Here's just a quick example of what a head on the side should look like, even if you're going for some sort of rounded chibi style (right now it really just looks like an oval) As you can see, you don't define the chin, nose, etc., and it therefore doesn't look very human. I would play around with the front area of the face more one you clean up the jaggies. In addition, I suggest defining the base even better by coloring it, adding in eyes+nose+etc, so that it's easier to visualize what you're going for, and can therefore work on the outlines to make them better defined as well.
Just my USD0.02. Would contribute my own edit, but I just barely had time to get my thoughts in a post before I've gotta head out for tonight. I'll play around with it tomorrow.
