In general, walking is the better exercise because it is a weight bearing exercise. A weight bearing exercise not only burns calories, it helps keep your bones strong too.
What you do for exercise really doesn't matter as long as it's something you keep doing. Remember, the exercise doesn't stop once we've lost the weight. If you want to maintain your good health as well as your weight, you need to be active in some way for your entire life.
If you enjoy the rebounder, keep doing it, but maybe add variety now and then. How about adding some strength training ? If you don't strength train, I'm going to recommend that you start with a day. increase your lean muscle. muscle burns fat. the more lean muscle you carry, the more efficient your body will be at burning fat.
Just doing cardio isn't enough. You have to watch what you eat as well as get some regular exercise that includes some strength training. Don't neglect your strength. And a workout can be very simple. All you need is a set of resistance bands.