As you've already stated, the drying or moisturising aspects and whether there are any ill-effects or other notable side-effects such as the oily residues or similar. I.e. you've pretty well summarised your answer within your question!
There may be people who take a more involved approach as to whether it dries the face, dries the neck (as the skin often behaves differently) whether any left-over hair is dry/moisturised/oily, whether there's a sheen left or a more matte appearance, whether there is any residues (oily/powdery/none), whether there is any discomfort or visible irritation, whether it causes breakouts or contributes to acne, whether it helps alleviate weepers... though that is a far more pedantic approach than most (myself included) takes.
I tend to use an aftershave or balm after shaving and most days otherwise I'll use a moisturiser so post-shave feel, as long as it's not uncomfortable, is mostly moot.