How do you decide whether you need to go to a massage therapist or a chiropractor?

Varies greatly. This depends on what you are trying to treat and who your practitioner is. For instance craniosacral therapy is done by some some massage therapists and chiropractors - good for various musculoskeletal problems. Generally, chiropractors work on joints(ribs, spine...). Massage therapists work on the soft tissue (muscles, connective tissue...). Ideally both joints and soft tissue are treated!
Depends. They offer the same thing - relief by massage and no diagnosis or cures. Massage therapist are gentler, work in a more comfortable environment, and will not attack you with unshielded x-rays or bogus theories. I would pick the massage therapist myself.