'They don't have anything else in common that would even warrant a comparison.'
I guess you could compare them on the grounds that they're both British imports with popular film adaptations fueling ticket sales, lots of kids in both casts. While Matilda is most certainly a 'family' show, it's more difficult to assign that label to Billy, although ultimately it did do well will tourists and families. I wouldn't rush to compare them in that light.
On the "girl's show/boy's show" note, I wasn't thinking exactly about the quantities of boys and girls in the casts. Yes, the ballet girls far outnumbered the boys in Billy, but it is fundamentally the story of a boy. Same can be said for Matilda, though I'm not familiar with the cast.
For the record, I'm not really sure if it's fair to call Matilda Billy Elliot for girls. I just thought it was a curious way of putting it.
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I know you.