Yes. For the posted image specifically, I requested a Norman Rockwell-style painting.

With Midjourney at least, it gives you four options and the ability to alter (“vary”) those options. If none suit your taste, you can rerun or change the prompt. In addition to specifying things in the prompt itself—there’s a wide latitude, left to its own devices it defaults to a kind of digital art style but you can override this with hard-coded options and/or specifying genres and media; I frequently use “oil painting on wood”, for instance, and you can specify styles (cubism, op art, abstract art, futurism, newsreel, photorealistic), color palette (dark, light, vaporwave, monochrome), media (giclée, daguerreotype, airbrush, tempera, canvas, wood, tintype, charcoal, ukiyo-e), and artists (da Vinci, Bosch, Escher [Escher produces fascinating results more often than not], Tanguy, Mead, Beksiński)—there’s a few arguments you can apply to the query. The one I remember offhand is, I think it’s called, “niji”, which specifically forces an anime-esque aesthetic.

DALL•E is similar, even showing you four options you can vary—but it’s much less robust in what it can do.

The tradeoff is, and this is why AI won’t be some silver bullet, the AI can’t take criticism. It can only handle so much information at once, and you’re kind of stuck with what ot gives you. A real person can be instructed much more precisely, and doesn’t have the pitfall of drawing hands awfully or making logical mistakes (multiple/impossible limbs and mangled hands are a frequent issue).

Here, give me a prompt and I’ll demonstrate. I have many credits to spare this month, I’m happy to show you.