What's interesting is when the new pic is shrunk down to a thumbnail, it starts to look even more like the original Sideshow pics. Just check CoolToyReview.com's news story on the new pics. The dark areas under the eyes seem to become more pronounced when the resolution of the pic is downgraded. So I think some of the issues with the likeness are definitely photography-related.
I've gone back and forth with the new sculpt pics and T2 Hamilton pics and I can't find anything wrong with things like the cheeks, chin, nose, or the structure of the face. Any perceived problems do seem to be based on comparing the sculpt with photos that are not at the same angle, hence distorting the appearance of the jawline or nose in the mind of the viewer. View the first pic below for one that seems to match the angle of the straight-on sculpt shot and you can see the chin and nose match up. I also think they have her hair color basically right, but it's missing the cheesy blond highlights that Hamilton appeared to have dyed in.
If there's any real strangeness to the sculpt, it's with the eyes. Hamilton appears to have bigger eyes in most pics. I think there are possibly two explainable reasons for this. One, the sculpt has intentionally given her a narrow-eyed expression with an intensely furrowed brow, as if she's squinting to aim a gun and pissed off at the same time. This might not be the best choice, since it's like a permanent action pose in the eyes, and one she doesn't use too often. The closest I can find to it online is the below.
https://www.dvdactive.com/images/reviews/screenshot/2009/6/t2skynetbdcap2.jpg
There she is narrowing her eyes from the brightness, although the expression is sadness, not determined anger as in the Hot Toys doll (yeah, I'm not someone who needs to pretend these things aren't dolls). Even here, though, her prominent eyelids remain slightly visible. On the Hot Toys doll, you can't see them at all. The only pic I can find where she's furrowing her brow SO much that the eyelids are obscured is linked below. Except here, she is furrowing her brow while holding her eyes wide open. The furrowed brow while squinting that the doll has is something I can't really find.
https://mikes-images.com/misc/t2/images/t2_mq_275.jpg
Another issue is that Hamilton seems to have more eye makeup on in the movie with longer, thicker lashes (Maybe it's Maybelline?). Look at this linked screencap to see them clearly:
https://mikes-images.com/misc/t2/images/t2_mq_069.jpg
I'm not sure how possible it is to reproduce that in a toy. It might start looking unrealistic if you paint the eyelash lines too long on the face, like on a Barbie doll. And you can't have them physically sticking out that much. I wonder if Hot Toys didn't go with the narrow-eyed expression because they thought it made the lack of long eyelashes less obvious than wide-open eyes.
Her eyebrows definitely also need to be darker and bigger vertically, meaning a thicker line than they are on the face now. Even when Hamilton had her strongest bad peroxide dye job going, her eyebrows remained very dark and only lightly trimmed. The ones on this toy are too narrow in shape from top to bottom and too light in color.
It's also possible the doll's eyes are too small or too sunken in. Hamilton's eyes definitely appear to be bulging out of her face more in most pictures than they seem to be on the doll. I think that's a subtle underlying sculpt issue and not something they will probably be able to fix. It wouldn't be like just narrowing or reshaping the jaw line or something simple.