This is a very interesting question to consider, and I have provided you below with links to the enotes study guides on both of these excellent short stories. My initial response to this question is to say that the biggest difference between these stories is the way in which the protagonist of "Her First Ball" clearly loses her innocence during the story, whereas in "The Destructors" we are presented with characters that have apparently already lost their innocence before the beginning of the story through the horrors of war that they have observed whilst growing up. They are clearly not innocent little children, as the anarchic lives that they live indicate. Whereas in "Her First Ball," Leila experiences a loss of innocence during the course of the story thanks to her conversation with the fat man as she is made to realise how temporary youth is:
Was this first ball only the beginning of her last ball, after all? At that the music seemed to change; it seeemd sad, sad; it rose upon a great sigh. Oh, how quickly things changed! Why didn't happiness last forever?
Leila thus comes to realise the temporary nature of youth and beauty during the course of the story.
Secondly, you might want to compare the cause of the loss of innocence. In "The Destructors" the moral delinquency of the gang is shown to be partly due to the war zone in which they have grown up and played. Note how they meet in an "impromptu car-park" which had been bombed:
One one side of the carpark leaned the first occupied house, number 3, of the shattered Northwood Terrace--literally leaned, for it had suffered from the blast of teh bomb and the side walls were supported on wooden strut. A smaller bomb and some incendiaries had fallen beyond, so that the house stuck up like a jagged tooth and carried on the further wall relics of its neighbour a dado, the reamins of a fireplace.
However, by contrast, in "Her First Ball," the cause of the loss of innocence experienced Leila is the inevitable passing of time and the way that beauty and youth will fade.
Thus, although both these stories concern the loss of innocence, you can argue that the treatment and discussion of this theme is rather different.