I think the biggest problem people have when drawing with crayons is that they regress to being five years old again. They hold the crayon like they're coloring again, instead of applying it like a fine art medium. Another problem is that many people want to make it perform like colored pencils. While similar in application, they are quite different. You should not use crayons and expect them to behave like colored pencils. You'll be setting yourself up for disappointment.
Mid_range pencils from brands like Staedtler or Faber Castel offer softer application, which allows you to get more color into the paper. This can produce a more vibrant color and reduces the chance of white flecks of paper showing through. Softer wax pencils are also better for shading and blending.