I was just listening to Aled Jones singing “Walking in the Air” and started wondering why it was so easy to tell it was a boy rather than a woman. What makes a boy’s voice singing the same notes so recognizable?
It’s just different. It’s not something that can be accurately described in words - if it was, there’d be little point singing at all. And anyway, how do you tell one woman’s voice from another’s? If that’s not difficult, then spotting a boy shouldn’t be a problem.
I can tell you from my own experience, though, that an adult male who keeps his falsetto in shape all the way through the voice-is-changing phase can sound indistinguishable from a female soprano, if he’s good.
Like GorillaMan said, it’s pretty much indescribable. This is my attempt, so YMMV. 
Keep in mind that unless you’re dealing with a castrato, in which case all bets are off, a boy soprano is young. His voice hasn’t cracked yet. But there are moments where his voice will have a slightly deeper timbre, a lower resonance–signs of the lowering to come; there’s also just an inherent masculinity in his voice, both which female sopranos, both kids and full grown, don’t have.
I don’t think that’s the best explanation in the world, but it’s as close as I could get.
Less vibrato, a “purer” tone, perhaps. Would relatively less training and, recording-wise, less over-production also have something to do with it? Plus, trebles typically sing a certain repertoire: often the solo part in anthems, for example.
There may also be some difference in their voice due to physical differences. The sound of a voice is not wholly related to the thickness of the vocal folds, some of the frequencies come from the shape and size of the rest of the vocal apparatus. Additionally, I imagine the shape and size of the rest of the body has some effect, though perhaps not much.
Having said that, I’m pretty sure that a well-trained boy soprano and a female soprano can be indistinguishable.
am I the only one who kept reading the title as “why can I buy a boy soprano?”
I’ve always considered boy sopranos to have a purer tone than most adult female sopranos. It’s just…tighter. More focused.
I would only buy one if I had a coupon.