Which do you think is more important for weight loss, paying attention to the calories we eat, or getting a sufficient amount of exercise?

It's not an either-or thing.
You need both in your life both during the loosing process as well as the maintance phase.

Calories certainly dictate weight loss.
It's important to make those calories good valuable calories rather than empty calories 98-99% of the time.

Exercise will tone you up.
Lower your glucose level.
If your glucose level is good it will help you maintain a good level.
Strengthen your heart.
Give you stronger muscles.
Enhance your mobility.
Decrease aches and pains.
Decrease your appetite
Increase your tolerance level when it comes to stress.
Help you deal with day to day situations much better.
Just help you feel a whole whole lot better.

Thanks for the long list of all the benefits of exercise!