One of the main differences between the two lists is the issue of "origin", a reflection of the respective country and culture. The New Yorker, for instance, feels the need to point out just how diverse the origins of its authors are:
The fiction being written in this country today is not necessarily fiction set in this country, or fiction by writers who were born in this country. Although all the non-native writers on our list have made a home for themselves in North America—some moved here as children, some as adults—the diversity of origins is striking: Nigeria (Adichie), Peru (Alarcón), Latvia (Bezmozgis), China (Li), Ethiopia (Mengestu), Yugoslavia (Obreht), and Russia (Shteyngart).These authors write of their diversity from a very American viewpoint, at once a huge plus and equally limiting. Much in the same way, it's written to an American audience (though the list includes Canadian authors). Nonetheless, they're doing what literature needs more of - diversity. It is worth noting the New Yorker's particular insistence to emphasize this notion - a magazine choosing to highlight the fact that their top American 20 Under 40 authors are from varying backgrounds (though all are, essentially American).
The Telegraph, meanwhile, downplays its own efforts at creating such a list, assuming because it does not resemble the American counterpart, it is less effective:
So with these potential problems in mind and in the hope of unleashing a debate similar in ferocity to the one triggered by the New Yorker, we are pleased to unveil our list of writers. We have used the same selection criteria as the New Yorker – all these writers are under 40 and all, with two exceptions, live in Britain – at least most of the time. But we haven’t controlled the types of writing, or worried about whether writers stand in some way for different experiences of Britishness. And we have frankly failed, if it matters, to achieve a gender balance – 13 out of the 20 are men – and most of these writers are white. But in other ways we have striven to be diverse, refusing to overlook excellent science fiction and genuinely good thrillers.
And yet that last sentence is key. The Telegraph includes authors that aren't just "genre-bending" (as the New Yorker puts it), but authors that do not strictly write in the so-called "literary fiction" category. Or perhaps it's just China Miéville who doesn't strictly fall into this category (or any category, for that matter...), but even the presence of this 100% not "literary fiction" writer makes the Telegraph's list diverse in a way that the New Yorker's just... isn't. The Telegraph offers the possibility that true talent might lie beyond the established novel and "literary" format. It's an important distinction.
The next difference is raised by the Telegraph itself:
The lists generated by the New Yorker and Granta are interesting as much for what they reveal about a country’s fiction as about the concerns of a writing generation. Though creative writing courses such as the pioneering one at the University of East Anglia have taken off in Britain, their presence is nothing like as pervasive as that of institutions such as the Iowa Writers’ Workshop in the States. [...] It is notable that most of the writers on the New Yorker list came though a creative writing programme – and many now teach on one.The question of creative writing courses is a fairly interesting one in itself and deserves individual attention. Still, the notion that creative writing courses are far more established in the U.S. doesn't actually show a difference in the writers, but in the culture and the accepted writing style. Again, this deserves its own discussion, but the rise of widespread creative writing courses, degrees, workshops, programs, etc. is clearly reflected in the style of books represented by the New Yorker as opposed to the Telegraph.
There are smaller, finer issues to be found in each list. Ultimately, these are two lists that paint a fairly broad picture of North American and U.K. authors. The authors' youth is both a help and hindrance to them - while some of these authors are established, their reputations are far from set in stone. Both lists are have merit, and while I don't take to heart too much of what is said (I will not be surprised if some of these authors publish, shall we say, bad books), I recognize some great names already. For that, kudos.