It's often noted, in discussions of the Death Note anime, that it's much weaker than the manga in its rendition of post-timeskip events partly for pacing reasons: the pre-timeskip parts of the anime adapt ~6.5 manga-volumes in 25 episodes, while the post-timeskip parts adapt ~5.5 in 12 episodes, so a lot more important detail-work is lost and the whole thing ends up feeling kind of perfunctory.
Much less often noted as far as I've seen, but nonetheless also true, is that the Death Note anime removes some important characterization-nuance from Light, starting right near the beginning, whose presence elevates the manga to be substantially better than the anime even before the time-skip.
In particular: the Death Note manga is, at its core, a tragedy in classic "character who has everything falls into ruin due to a fatal personal flaw" style. Light is a brilliant student who, in the future ahead of him, has the potential to do practically whatever he wants. He's driven to ruin by the fatal flaw of unwillingness to admit, either to others or to himself, when he's made a mistake. This flaw is an essential piece of his characterization, in the manga. And the anime pretty much entirely skips over it.
As portrayed in the manga, Light's decision to become Kira—which ultimately leads to his downfall—is made in the following way. First, he finds the Death Note, and is led by morbid curiosity to write a name in it, killing someone. Then, still not really believing it, he kills a second person too. At which point it hits him that he's killed two people. And at that point, after a viscerally-horrified breakdown about what he's done, the inability to admit mistakes kicks in, and he proceeds to rewrite his own value-system such that it yields the result that killing those people was actually okay, and in fact morally good. Because the alternative would be for him to acknowledge himself as having made a terrible mistake, and that, more than anything else, is something he's unwilling to do if he can see any other option at all. And then, having convinced himself that those two murders were good, he proceeds to reason that, if they were good, then doing more like them is good; and thus he becomes Kira, leading eventually, far down the line, to his ruin. The anime, by contrast, substantially deemphasizes this flaw of his, portraying him as much more calmly put-together through that series of events and thus making him come across as having been tempted in becoming-Kira-ward directions all along.
Similarly, in the anime, when Light leaks a bunch of information to L about his identity by using non-public information acquired via police channels, he declares that actually this was deliberate as a means of baiting L out so he can kill him, and the anime presents this declaration pretty uncritically. The manga, by contrast, presents it as an extension of that same character-flaw: Light is unwilling to admit to having actually just straightforwardly messed up, and therefore makes up a new plan to view himself to have been following-all-along, thus leading him to take more risks in his game against L going forward and thus, once again, helping him along the path to ruin.
Et cetera.
Compared with the manga, then, the anime's version of Light's characterization ends up less interesting. And, moreover, it introduces a plot hole, when the Yotsuba arc comes around! It makes it much less clear why an amnesiac Light would be so straightforwardly aligned against Kira. In the manga, this is pretty clear: a Light who never killed anyone wouldn't have rewritten his values to consider killing people to be good, and therefore would look at Kira as straightforwardly evil. And, in fact, his amnesiac self has trouble taking the possibility of his having been Kira previously, even as the evidence starts building up, because becoming Kira would be a mistake according to his value-system of the moment, and this leaves him having a very hard time contemplating the possibility of its having in fact happened! Whereas the anime, by deemphasizing Light's big flaw, makes his amnesiac-self's differences from the way he is for most of the story up to that point come across as much more out-of-nowhere, much less narratively well-founded.
So, overall, the people who talk about the Death Note manga as superior to the anime specifically post-timeskip strike me as somewhat understating things. The manga is superior to the anime pre-timeskip, too, via that extra layer of characterization and a resulting improvement both in character-interestingness and in plot-coherence. And thus I consider the manga to be very much the definitive version of Death Note from start to finish, despite the anime's relatively-higher popularity.
