More mAh means more weight. I tend to stay in the 5000mAh-5500mAh range because of that.
But you are correct. More mAh equates to more discharge rate. But it depends on the C rating as well.
Here is the math using advertised C rating:
30C x 6200mAh = 186,000mAh ÷ 1000 = 186A constant discharge.
40C x 5000mAh = 200,000mAh ÷ 1000 = 200A constant discharge.
35C x 6200mAh = 217,000mAh ÷ 1000 = 217A constant discharge.
But there again, advertized C rating and actual C rating are two different things