I mean, these things are multimodal. For most people it's easier to cut enough calories to lose weight than it is to exercise enough to lose weight (though both are physically possible). But, of course, if you are losing weight you should be exercising! It's the best way to retain muscle mass, which is vital for health.

I am sure that when I've lost weight it's more the portion control than the exercise - but the exercise is a critical component. When you go from being sedentary to doing even casual exercise you feel better and get more energy - which you can then use to be more active. Without some kind of virtuous lifestyle-change cycle you are likely not going to shift your body mass, kind of no matter what ultimately puts you over the edge.