Try the Zombie and Skeleton NPC templates.
The list of monster pairs like what you're looking for is very short, and reverse-engineering the differences might be more hassle than it's worth. I recommend an alternative that I've used for the same goal of creating zombie and skeleton versions of arbitrary monsters.
The Dungeon Master's Guide provides templates on page 282 for modifying an existing NPC to change its race, including monstrous races. This information is presented in a section on customizing NPC's and does not mention customizing monsters, but there is no mechanical or rules difference between an NPC and a monster, so the technique is usable in your situation.
I'm not going to reproduce the material in the DMG for legal reasons (it's not open rules content), but the zombie template specifies increasing and decreasing certain ability scores and adding some features common to Monster Manual zombies including the Undead Fortitude feature and darkvision. The skeleton template works similarly.
Keep in mind that modifying animate dead in the way you describe will increase its power and could cause balance issues. However, the zombie template should represent how the 5e designers themselves would start creating a zombie version of a monster, pending playtesting and refinement.