Regarding the "exercise more" strategy:
It's true that you just need to burn more calories than you take in to lose weight. But it's far easier to create that caloric deficit by limiting/changing diet than by running a whole bunch. There are a lot of downsides to trying to "work off" your bad diet, including overuse injuries and overtraining, burnout, etc. In addition, diet has an affect on more than just body fat %. You might be able to "work" your way down to 5-6% body fat with a crappy diet, but you won't necessarily be very healthy and your athletic performance, moods, and energy level won't be ideal. If you want to run a lot that's fine, but I wouldn't start trying to balance too much food with too much exercise. Losing weight is one of those rare things where you can achieve your goal by doing LESS (eating).