Ok, let take a step back.
Your talking about the ability to play mucsic from a score without making mistakes. My computer can do that, and it sounds "horrible". Yes it's enough when playing around with scores to hear if a chord matches, or if a certain passage sounds the way I want it to, but it's a far, far, cry from good sounding music.
A lot of musical instruction (including top notch schools like Julliard) tend to be failing at teaching this most important difference. Music is an expression of thought, emotion, and ideas, not mathematical reference points, tones, prescribed chords, and technical ability (to play exactly what is written).
A wonderful, awesome playing of "music" may have 80%-90% mistakes, and still sound wonderful. It's about the piece's ability to convey then it is if that C4 is a perfect 261.63 Hz.
So just because a person (especially a child) can play all the "notes" correctly, doesn't mean they understand or can even correctly convey an emotion any better then my computer can.
If you have every listened to a passage that made you laugh or cry, or truly made you feel a strong emotion, then tries to recapture that emotion by listening to different people play the same piece, you will understand.
A child can not understand religion, worship, and reverence how can they possibly play "Requiem". Sure they get the notes right, but does it stir in you the feeling of being in church and undertaking some holy and sanctified ritual? Does it make you feel like your at the same time, "playing" with the ritual on the very edge of sacrilege. These are not concepts that a child has the capacity to understand. Keep in mind that every "player" will add their own baggage as will the audience. A person needs that baggage to be able to play decently, and that baggage comes with time.
So, yes, can a "child prodigy" smack the whites and black with more accuracy then Mozart? Probably, because every musician will tell you for 100% certanty, that technically being correct is not really what music is about, so I doubt he focused on it very much.
What he was good at was conveying emotion, beyond his years in some cases, in his pieces and playing. And while we do have child prodigies that can do that now (or at least in modern history), it's a far cry from what a lot of people stick the label on today.
One last note. For any "prodigy" or famous person, be it Mozart or Steve Jobs, there is also the "need of the world". Someone would have been a Mozart even if Morzart himself didn't exist. The music world needed one. It needed someone to facilitate the evolution of music. That's not to say it's all timing and he was "average", I just mean that there is always a component of "need" in there when someone like a Mozart is created.