It is much easier to lose weight if you can get restful sleep. My manager lost 20 pounds after he got the CPAP machine with no other lifestyle changes. He had more energy and improved metabolism when he wasn't constantly tired and subjecting his body to low blood oxygen for 1/3 of the day.

So this isn't an either/or situation. Sleep apnea can also be a contributing factor in being overweight. So do everything: take steps to eat better, sleep better, and exercise more. Small steps in a number of areas are often better than a big step in just a single area.