The lighting in the top one's much better, but it still feels inconsistent. The top one also has the best colours yet, in my opinion.
I made in edit, though I worry I didn't interpret everything in your image correctly. I hope this and my wall of text helps!
The first thing I did was decide where to put the light source - looking at the existing shadows on the face, I decided top right, slightly from the front would be good.
Since the light is in the upper right, that's where the highlights on each object go. The brightest part of the hair is in the upper right, the folds on the skirt are brightest on those surfaces facing the upper right, etc. Conversely, the lower left areas of each object are in shadow, because the light doesn't get there - the bulk of the object gets in the way!
In addition, some of the shadows are cast shadows - shadows cast by other parts onto surfaces that would otherwise be lit. For example, the tops of her legs are in shadow because the skirt blocks the light. The tops of her arms are in shadow because the blue shoulder-thing blocks the light. The little irregularity in the shadow on the shoulder-thing is the shadow cast by her hair. More subtly, the shadow in the middle of her torso is a combination of her chest's form shadow (parts of the chest face away from the light) and the shadow cast by her chest. Originally, the shoulder-thing cast a big shadow on her chest, but it looks to me like it should rest right against her skin, so it wouldn't cast much of a shadow on the chest, hence her chest being mostly in light in my edit.
I redrew the face to have clearer features - a nose, a mouth, more realistic eye placement - the original eye was lower than the nose! I reduced the pile of hair in front of her forehead and gave her more volume in the back of her head, which I think made for a good compromise between looking believable and being chibi. I tweaked her hands a little to give a better impression of fingers and thumbs. As with everything else in this edit, these changes are not necessarily "better" than your own style, but perhaps seeing the same thing in another style might give you some ideas for your own style.
With the hair, I wasn't sure what the reddish colour was meant for, so I drew it as a red streak in her hair.
Probably the most complex change is to the skirt. I wasn't sure what you were going for, so I interpreted the light streaks as highlights from folds/ruffles. I decided to play that up by making the skirt ruffles. I changed its outline to suit (just a wavy line, really), then added highlights to the right part and shadows to the left part of each wave. The highlights get smaller towards the left as there is less light there, since that part of the skirt is facing more away from the light. On the furthest left wave, the one that's right up against the left edge of the skirt, there's no proper highlight at all, just a break in the darkest shadow.
You'll notice that the bottom of the skirt, despite being wavy, has a sort of arc or bowl shape. That's because the skirt is essentially a cone that we're seeing from slightly above:
You were right that the white/blue frills are tough in that space. In these instances, it's better to sacrifice some detail for a clearer shape. I drew them by making another wavy line, but with smaller waves, and repeating basically the same light/shadow process as with the skirt, except the skirt also casts a shadow onto the frills, so the highlights are just along the very bottom.
Lastly, I changed some of the colours. I made the middle skin colour a little more saturated because it looked a bit dull for a skin colour to me, and I made the blues more purpley, so that they don't stand out as much. I changed the two greys on the eye into purples from elsewhere in the image, because it looks nice and there didn't seem to be any reason to have two whole new colours for such a small area.
If I didn't explain something well or if you're not sure why I made certain changes, feel free to ask!