I've read studies on this, and the general understanding is that it takes BOTH to be successful (that is, losing the weight AND NOT gaining it back...)
HOWEVER -
I know my own body. When I was younger with a faster metabolism, I could skip a meal here or there & eat yogurt for breakfast & lose 5 pounds in a minute. (not a LITERAL minute, LOL). The only exercise I got was P.E. class, but hey - that's about 45 minutes a day, 5 days a week... otherwise I was a lazy teen.
Then in my 20's, out of college & into a SITTING DESK job, I gained a little here & there. I was pretty good about exercising. It was good for about 5 or so pounds gone. But that wasn't enough. So I tried dieting. That didn't really help too much. But when I did them TOGETHER -
"wow wee, looky at me! skinny as can be & I feel free!"
Then in my 30's... lawd hep'me! - I could diet til the cows came home, but if I didn't exercise, I wouldn't lose ONE SINGLE POUND. So I just started exercising LIKE CRAZY. But NOT dieting. I still could not lose ONE single pound!
So in my 40's now... I have learned... FOR ME... it takes BOTH. However, recently - like about 3 weeks ago! - my doc told me that dieting will make you lose the weight; exercising will help keep it off. So yeah... I agree with the 80/20 deal. 80% food/calories, etc. & 20% movement.