Shadow quality generally improves with increased shadow map resolution (i.e. shadow edges are less "jagged"). I noticed this is also true for shadow maps with resolution far greater than the viewport (screen) resolution.
High-res maps like this are sampled at the lower frequency of the viewport resolution, and as such are akin to texture minification. (Assume point-sampling for simplicity.) Furthermore, minification exacerbates as the camera moves further away from the shadow, resulting in pixels "covering" multiple shadow texels.
Texture minification normally produces aliasing/shimmering artifacts, so I fail to understand why this is not the case with high-res shadow maps as well.