Anecdote here, but I've found that for me the key to weight loss has been exercise-first. I decided that I'd never be very good at reducing my dietary input (I really enjoy food) so I focused instead on increasing my energy output by incorporating progressively more physical activity into my lifestyle.
Over the past few years I have steadily and gradually ramped up my activity through walking, running, cycling, body-weight exercises, plyometrics, stand-up desk, and so on, and I've been progressively losing weight and feeling better physically, mentally and emotionally. As a result, other complementary aspects of health - sleeping, eating - have also tended to fall into healthier patterns in a positive feedback loop.
It's hard to believe that exercise isn't the key to weight loss when I burn 2,000 calories on my Saturday morning run.