My son is a huge reader - currently working his way through Alex Rider, he's read Potter, the Pullmans, Cressida Cowells, Lemony Snickets, Pittacus Lore, all manner of modern kid's novels. It's not that he doesn't read - he inhales books - he just doesn't like older books. He finds them boring. 
I don't know. Maybe the imaginative worlds they create are too long ago, now? He's high functioning ASD as well so that may be why. I'll have to hope for more interest from DD! She's into imaginative play, which he never was at all (think of the extreme male brain theory of ASD, essentially...) I loved sharing Harry Potter and Star Wars and so on with my son, but most books from more than 30 or 40 years ago have been misses, to date. Maybe he's too young for them, too, and a more modern style is easier at this age.
We have the Mopurgo books - will give that another go, thank you. He did like Stig of the Dump when we had it as a bedtime book a few years ago; will try and see if he will read it now, too. When Hitler Stole Pink Rabbit is in the shelves but I am nervous about that as he's an anxious child, and while he's immune to fear in fantasy, Hitler was very real, and DH is Jewish... so maybe a bit small still. He won't go for the Borrowers - tried that. Wouldn't do any Lynne Reid Banks, either. 
The Four Story Mistake was recommended on Amazon - will have a relook! I also bought The Tree That Sat Down and one about a snowball because of MN recommendation, which sit in the shelves, so will have a look again and see if he might like them.
His favourites are things like Who Let The Gods Out? Modern, preferably comedy, and always adventure. But he is young still, so hopefully as his horizons expand, so will his reading tastes.
Loonoonow I loved Anne of Green Gables as a child... then reread them again recently and was so disappointed. It hasn't aged that well to me past the first few. The later ones are not great. Rilla of Ingleside is abysmal. She had a heartbreaking life, though, the author. I suspect the books reflect that loss of hopeful realism and joy, as they collapse into trite sentimentality. I can sort of understand your DD's feelings. And as for What Katy Did - they joined the Twilight series, as books I bought for the kid's shelves, read, and actually binned. I didn't even want them returning to the charity shop from whence they came. Just awful messages for kids on relationships and values (and at least What Katy Did was Victorian...)
My real sadness was the lack of interest in Laura Ingalls Wilder. I so loved those books as a child. They opened a door into a wholly different life. Again, perhaps I should try again as he rejected them a year or so ago.