The two links to the vectors on Advanced Anime look alright at first glance, but upon closer inspection I notice that
all of the lines on each are very jagged. This often gets vectors/items deleted, so I'd suggest looking up more
effective ways to vector. Since you're a Photoshop user, try this tutorial out: Here
As for the first thumbnail you've post, it's alright but it has noticeable compression artifacts. This is
something that happens at times when saving something as JPG, JPEG. Look up how to better save and compress images in
Photoshop- a lot of people run into this issue actually, even me. If you don't know what I mean about compression
artifacts, here's an image example: Here