An important thing to remember, though, is that these things are really, really hard to study. The meta-analysis is likely to be negative information in how accurate it is. "deliberate practice" is not a valid term, you can create a whole new field to figure out what it means to "deliberately practice" for any given thing, and there's no evidence whatsoever that we're any good at it. We're trying to measure the efficacy of something the purpose of which is... well, that very thing.
I'd posit that the entire discussion is absurd...
What matters more depends entirely on where you stick your goalposts. That is, it doesn't matter at all. The question doesn't actually make sense.
Hard work matters... among people who are extremely similar to each other. And if we take the hypothesis that hard work is also genetic, it's yet another trait by which those two people are actually different. Outside of the equal genetics factor, hard work matters in a given genetic composition vs hard work in another genetic composition. Very boring equation: genetics1 + hardWork1 vs. genetics2 + hardWork2. Each of the 4 values has a max. Which one matters more? What a silly question! Depends on what the values are! We even have a saying for this: "Hard work beats talent when talent doesn't work hard."
Genetics matter so disproportionately that the only reason the genetics vs hard work discussion can hold at all is because we're always having it within carefully defined goalposts around some area we're unsure about. Hard work is, effectively, always given value in situations where genetics are perceived to be "equal enough". The Sports Gene has a section on women in sports and all the interesting implications that entails. It's fairly obvious to everyone that women can't compete with men on, say, physical strength. And people without legs can't compete with runners. Usain Bolt is nowhere near as fast as a cheetah. Let's not talk about Down Syndrome. All that should have shut down the genetics vs hard work argument long time ago. The only reason it didn't is because we moved the goalposts.
Because as long as we move the goalposts, we can keep things interesting. As long as we don't know why someone won, we can get excited about it. We can talk about hard work, dedication, cunning, special approaches, whatever we want to do. It's all dice in the end, but as long as we don't see it, and as long as we can fool ourselves, we love it. We want the randomness. We want to be surprised. Azart.
I'd argue if you're actually trying to measure something, not merely entertain yourself, you don't get to keep moving the goalposts.
But the absurdity is just beginning.
Genetics and hard work are hilariously inferior to information.
I can read and write, because that has been granted to me by society. I can tell a computer what to do, because that framework and profession was created for me. I can lift weights, because someone told me I can. I know where I am, because someone made me a map. I have a chance of learning quantum mechanics, because someone was there to describe them, perhaps even in ways that someone like me can understand. Consider the weight of that: a person with inferior genetics and inferior hard work can get a free informational transfer* from a person with superior genetics and superior hard work. No person of the past, no matter how intelligent or hard working, has any chance against that...
This is also why "deliberate practice" is such a tautological concept - a lot of it is information dependent. If you have much better knowledge on how to practice something you can go a long way.
It gets worse.
People without legs can't compete with runners. I just said that earlier. Well, unless they get metal legs... creating so many problems for people who are now trying to figure out what that means and where we need to stick the goalposts next time. [The whole concept of "cheating" implies goalposts.]
People with certain mental illnesses can't do a whole host of things. But if they can get certain medication and therapy, they suddenly can.
People had genetics to be tall, but they ate so poorly it didn't matter. [the article touches on a few things like this and refers to them as environment, but I think the overall thing is a lot wider]
Athletes engage in some interesting substances to boost performance in ways never before possible.
I can't outrun a cheetah. I can't fly like a bird. Doesn't matter how hard I try. Will never, ever happen. Nobody would even suggest it. I don't have the genetics for it. Doesn't matter, I have an airplane.
My memory may be poor, but I have notes and my phone and lots of other tools. My eyesight at night may be bad, I should be sleeping at this time, but I have the electric light.
The degree to which my fate is affected by information and causality is obscene. In comparison, my hard work, even my genetics, are nothing, beyond the very fact that I am a somewhat healthy human, which is also a product of these very things.
Why, then, are we in such despair? We're improving at an alarming rate! Maybe we're not getting more intelligent and our genetics are not getting that much better but we're still so much more capable of actually achieving things than our ancestors. Why is this so invisible, and why we care so little?
Well, because of competition. When we improve things, we often do it across the board for a large area. Not all that fairly, not all that proportionately, but, at the end of the day, almost everyone gets access to that Wikipedia webpage, and almost everyone gets access to that car. So the things that matter the most, apply to everyone, and the only thing left is the small portion that genetics and hard work take up. Because we've equalized everything else, and because we can't be satisfied with merely just living better, we have to find that last small portion and decide based on it who deserves to live how, because there's simply nothing else left.
For those who understand it, it promotes hoarding power and information. Promoting the notion that hard work or genetics is all that matters moves the attention from the more important things. And that's why you'll never get a clear answer on the whole genetics thing because information and causality absolutely, unambiguously matters. That's probably your Flynn effect. It only doesn't matter in your eyes because you are looking at people who both got the major benefits so genetics and work start kicking in.
We could be elated that we have more children than ever who can read and write, we have so much information available freely that the informational transfer is staggering, we have so many means and tools that modern high school athletes are beating Olympic athletes of the past. This is far greater progress than genetics could even dream of. We could understand how this was all achieved, and how much is gained from every individual person growing, pool our resources, research ways for better information transfer, discover new information, and develop superior tools and enhancements for the human.
But, instead, we're worried about whether or not this particular human can run 1 second faster than this other one. And we agonize over this meager improvement and how to get it. And how to promote it. Because we decided only the very best one deserves anything. We're looking for the diamond in the rough because we don't think the rest of humanity deserve it, all because they're not contributing 100% to a .00000000001% of their fate.
Can you become a musician? Maybe. Maybe not. But don't limit your options to just work and genetics, there are more powerful forces in this world.
* Disclaimer: some amount of intelligence and work required.