For the most part the second one is definitely better drawn, but there is one or two things I'd like to point out which might be why some people like the first one better, namely her ear and her forehead.
Her ear is a bit to far forwards, if you follow your jawline with your hand it goes almost exactly to the base of your earlobe, as it is, it kind of seems to end in the middle of her cheek. As for her forehead, personally I think it just slopes too much too quickly.
So, while I think the art is overall better (I mean, in the first one I don't think she even has ears ) those little issues kinda mess it up IMO.
I think it's a lot to do with the facial anatomy. While the first one is not quite bang on, the second one triggers a very different, and less relatable response. The anatomy any symbols used in the first one is easily interpreted as "cute" but the second one is "uncanny" and almost alien-like. The line quality and coloring is nicer, but the over all anatomy, while not necessarily "worse" is a lot more awkward to look at.
I think a lot of artists go through this sort of strange stage in their improvement where, for a while, their symbol set hits a kind of dive, and the elements all together actually look like a backwards step as far as improvement goes. But in actuality, the understanding you might be a lot better than the understanding you had then--it's just not yet coming together in presentation. Think of it as the "awkward teenager" phase in stylistic/artistic development :]Keep doing studies, you're on the right track.