I've been trying to look into this deeper, knowing that I basically set up a false dilemma to simplify the situation. There's cute, then there's realistic, and there's a fair number of things in-between. For the sake of argument, I'm going to set up a sliding scale from cute to realistic.
*Pardon if I come off as bullshitting. These are just my obervations while I'm trying my best to look into this*Searching through deviantART for what is popular there, I found some things that actually challanges my thinking.
Tier 1, I will stick anything with chibi-proportions into this tier. This is a 'pony', but stylized to an extreme that it doesn't look anything like the original animal:
http://fav.me/d7q8v9e However, there is not very many pieces I can stick on to this extreme
Tier 2, which I'll stick in your usual 'anime' style. The face is stylized to exaggerate youthful features, but with *relatively* realistic body proportions:
http://fav.me/d7qey6qTier 3, moving closer towards realism, I'm a little confused here, but in this tier, I and will stick both this Japanese style
http://fav.me/d7obm2l , and this western style in the same tier:
http://fav.me/d7rym4nTier 4, i'm going to stick here, something I'd call 'real' but cautious knowing that proportions are still highly stylized:
http://fav.me/d7qvjg1Tier 5, is what I'll stick as a reasonable extreme for a realist painter, but an actual painting took a while to find among photomanipulations:
http://fav.me/d7qhwkfFirst, a word of caution that my experiences on deviantART will put a clear bias towards more realist styles since it's full of artists - people are more likely to appreciate the work put into a realistic style. Again, I found these mostly from what's popular on deviantART in the past month, but what I was surprised was I found a lack of art on the cute extreme, but also on the real extreme as well.
From experience, art styles leaning on the extreme end for cute runs into several issues.
- It is more difficult to create something memorable with more extreme cute art. My sister told me of a moe-style artist who got away with tracing for so many years, and I was not surprised. The face style they traced were done in a popular (but IMO highly generic) moe style, allowing the tracing artist to get away with art theft for years.
- Cuter art styles are arguably pretty over-saturated as a result too, if said artist got away with tracing for THAT long. Might also be why the only 'extreme-cute' art happens to me MLP fan art, and not those little chibi dolls you see all over pixel artist circles on dA

- Limited on striking compositions, animations, and costuming with the most extreme chibi proportions. This might explain why there's more tier-2~3 art that's popular on deviantART because there's a larger body size that gets you far better potential for good composition
That might explain why I found less 'extreme-cute' than I thought there would be. Most of the art that makes it up high in my search results actually falls somewhere in the middle from cute to real.
However, cuteness at around tier-2 is still hugely popular if you have entire imageboards catered to the otaku subculture, such as this:
https://danbooru.donmai.us/explore/posts/popular [warning: explicit images!] I also don't take much interest in anime, but I'll tell you that I think that the art found there is pretty damn generic.
I wanna say that I find most potential around tier-3 where I stuck in western-style illustrations, particularly styles that enjoy a great deal of creative liberties with face shapes and cuteness is not always a goal. However, cuteness is still highly possible with the given art styles, just that not every character has to be cute.
I'm still looking into this, but this is where things have brought me. Cute is good, but going for cute comes with its own challenges