Hi Ryan. Since your question asks specifically about ‘exercise’ only, I will relegate my answer to exercise.
In my opinion, one of the best ways (exercise-wise that is) to lose weight is to exercise at the highest intensity that a person can SAFELY exercise. The definition of “high intensity exercise” is RELATIVE to each person, but has been proven to give you a greater caloric expenditure per unit of time. So, assuming that the time element remains constant (i..e. if the person has 45-minutes to exercise, then they still exercise for that same duration but at a higher than normal intensity) then their caloric burn will be consistently higher. The MAJOR issue with higher intensity exercise is that it is NOT for everyone. Due to the higher intensity, the risk of injury is also higher, so this type of workout must be closely monitored, and should NOT be undertaken without the approval of the person’s physician or healthcare provider.
I hope that this helps.