It does look better.
But, I don't think dreamisle meant for you to use his/her edit. In fact, I think it's pretty much frowned upon by everyone here. You should understand what he is trying to tell you and study the edit to make your own.
Your strings are far too overAA'ed, they're a blurry mess, and what you have doesn't even get rid of jagged lines. Since your background is transparent, I don't think it's a good idea to AA them at all, just leave them as thin 1-pixel thick lines.
I'd say it's okay to dither when you really need to, not when you just feel like it. In order to understand better when to use dithering you should read some of the tutorials on dithering out there and study some great pieces that use it effectively. Most of the time it's used subtly and discretely. It's often used to make a transition between 2 colors, when you don't have another color in between. Other times it's used for texturing. There are many more patterns than your standard checkerboard pattern, too.
Anyways, if your piece isn't good to begin with, I don't think dithering is going to make it much better at all.