As far as I know, the angle setting is designed to visualize stretching of each individual polygon in your UV map. I don't use this one very much since that information is rarely consequential when using Blender's unwrap tools.
The area setting, on the other hand, visualize the relative size of UVs relative to their mesh counterpart. This setting is very useful. If all your UVs are blue in the area visualization, it means all UV sizes relate 1 to 1 with your mesh, which is a good thing. When you see yellow or red, it means those polygons are significantly different in size UV space vs 3D space.
This can be desired but often isn't. For example if I'm making a character, I may want the face UVs to get more texture resolution than other less-important areas (like the bottom of the feet/shoes). Most often though, I want to adjust all UVs to be blue in color so I know they correlate in size to the model.
