I'm trying to decide what sort of similarity measure I should use.

• Roughly speaking, when should someone use the dot product to assess similarity between vectors?
• Roughly speaking, when should someone use the norm of the vector difference to assess similarity between vectors?
• What are the pros and cons of these approaches?

I'm not looking for a specific answer on which one I should use for a specific problem. I'm wondering more generally about when these approaches should be expected to work well.