Wonderful work on your first assignment.
Your assignment is a little unusual in that I don’t find your “beast” photograph to be terrible at all. In fact, it has many strong design elements that are different than your “beauty” photograph, but are nevertheless still interesting and engaging.
The major difference between both shots is the sense of depth and layers. I think this is what your main point was with your varied compositions. And you’re right that creating the illusion of 3 dimensional space within a 2 dimensional photograph is one of the keys to creating great photographs. However, your first image (i.e. the best), lacks that sense of depth but it’s not poorly composed. In your “beast” image everything is flattened into 1 layers, but you’ve used color, shape and line as visual elements to help organize and structure your composition. My point is that the composition of the “beast” image doesn’t look haphazard or lazy. You used a strong yet simple color palette, you’ve used a leading line to bring your viewer’s eyes into the photograph and as stated above both line and shape help give your image a style on its own.
Overall, great job on both photographs. I look forward to seeing what you do next.