Dissect
Focuses on the physical act of carefully cutting something apart to examine its internal structure. This is typically done with a scalpel in a biological context, but it can also be used metaphorically for breaking something down into its component parts.
Anatomize
Implies a deeper analysis beyond just the physical separation. It involves examining the structure and relationships between the parts, often with the goal of understanding how something works as a whole. While dissection can be a part of anatomizing, anatomizing goes a step further.
Analogy
A biology student might dissect a frog to learn the names and positions of its organs. A writer might anatomize a character’s motivations to understand their actions and psychology.
Summary
Dissect can be used figuratively for a more critical or negative analysis, while anatomize usually has a more neutral connotation. Anatomize is less common in everyday speech compared to dissect.