Looking around, I've found a lot of research on the allometry of visual acuity and vision at a distance, but not so much on vision close-up. As I understand it, the "near point" of vision is largely determined by the optical/focusing power (diopters) of the lens, which is itself determined by the refractive index and lens curvature (lensmaker's equation). Assuming the refractive index is constant, this implies smaller animals should have the more powerful vision (assuming smaller eyes) necessary to resolve something as close to their eyes as their own claws. Does measurement agree with this hypothesis? What is the scaling relationship? Is there a single one, or is it sensitive to eye type like acuity is?
Exciting question, and anticipations are largely met for mice (featured in title). Mice have a closer focal point than humans. As less than 2 cm they can likely see their fingers. Assumption on constant refractive index would require to further assume that viewing angles are different as numerical aperture changes. Mice having a more powerful vision system could be considered true.
Recent publication with measurements underlying above: https://doi.org/10.1364/BOE.3.000715
Generalization beyond mice would be interesting, but likely require control for other things such as habitats and whether predatory animals, ....