The fat-burning zone is a myth. More intensity is better than less intensity. As a general rule, you want to find the most intense level of exercise that you can maintain for the period you want to exercise. Or do intervals, which allows greater intensity for shorter periods.
(The fat-burning zone myth turns on a misconception: while it is true that at the lower level of intensity a greater % of the calories you burn will be from fat, it is nevertheless even truer that a higher level of intensity--'cardio zone'--burns more calories overall, including calories from fat. For example, when you're sleeping, your body is running almost entirely from fat calories, but it would be ludicrous to suggest that sleeping is better exercise than running...)