Focus on Diet or Fitness

You use your diet for weight control; exercise is for fitness.

Both in combination as diet is about calorie deficit and fitness is good for your overall health. Which one is important is your choice

If i workout i tend to get hungrier and want to eat more.

That's natural and to be expected. You need more energy to support those activities. Also your "calorie limit" goes up when you exercise so you can eat more and still be at a deficit.

It's often said that you diet (or count calories) to look good in clothes, and you exercise to look good naked. Also, you can't outrun a bad diet.

It's a little more complicated than that, but not much. You lose weight because you are eating fewer calories than your body needs. However, if you're not using your muscles, your body will effectively say (if it could talk), "Hey, those muscles aren't getting much use. They have protein that I could use to keep the rest of the place up. Let's grab some of that protein and repurpose it." So if you don't do at least some exercise, some of your weight loss will be lean body weight (i.e., muscle, since you won't lose much bone or connective tissue).

Hence, it's a good idea to do some resistance exercise (google body weight exercises for some basic routines) and cardio (for endurance) as you lose weight. Make sure to eat enough to cover the extra work, but beware of eating too much, as has already been mentioned. Plus, websites, fitness equipment, and even heart rate monitors tend to overestimate calories burned in exercise, so be conservative in your estimates. I did a lot of exercise in 2012 and gained 10 lb. I did even more in 2013 and lost weight, because I was counting calories.

I have been using both, but my first focus has been on diet. I am a carb-hog and I know that if I don't watch it, that macro can consume my daily calories. I used to struggle with bringing my carbs under control because I wasn't strategizing about what i would eat instead of carbs. Now I'm focusing on a protein centered diet with a secondary focus of making sure I am getting a good balance of dietary fiber so that the carbs I am consuming have more overall nutritional value. As for exercise, I had an epiphany last year that the greatest source of my body image issues is my body composition rather than just my size, and the only real way to change my composition is through exercise. I love swimming and dancing, so I have been finding resources, like joining a 24hr gym, so I can do activities I love and can keep up. Diet will probably get you in the ballpark you want, weight-wise, but probably for the definition that your mental image is striving for will only be achieved through changing your body fat composition and building muscle definition.