They tell different stories, make no mistake. Watching the movie will have next to no effect on your ability to predict just what'll happen next in the novel, but that's no criticism of either. As paired visions, it's hard to think of an original/adaptation pair diverging this widely that are both so very, very good.
The Children of Men is my last first read for next term's extinction fiction course, which we'll cover second: 25 years since the last human child was born, but somehow it'll be the happier of the two novels we read in our "Hope in the Dark" module:
Pleasure need not be less keen because there will be centuries of springs to come, their blossom unseen by human eyes, the walls will crumble, the trees die and rot, the gardens revert to weeds and grass, because all beauty will outlive the human intelligence which records, enjoys and celebrates it. (p.9)This is a society, a civilization, a species living without hope, and as such it has gone irrevocably mad. Its members veer from celebrating the transitory signs of life (the birth of kittens, especially) and the symbols of motherhood (an intense, wide vogue for pushing dolls in prams), to the very worst kinds of crimes, committed in a state of horror at the inconsequentiality even of those actions from which ought to trigger against the sinner the most absolute of consequences.
But in the 1990s, when P.D. James was writing this novel, most Western nations were all a-flutter at the consequences of declining birth rates: the challenge of financing pensions for an ever-larger sector of society, a lack of applicants for entry-level jobs, a surfeit of qualified managers, all of which indicated a coming need for (drink your gin, quickly!) immigration from the (good lord, no!) brown countries.
Before the mountains were brought forth, or ever the earth and the world were made, * thou art God from everlasting, and world without end.The Children of Men works really well as a parable, and for multiple themes religious and political, too, so it's not purely an abstract novel. But as with every good parable, nothing good comes from reading the novel only as parable. You've got to luxuriate with the characters wherever they find their pleasures, fear with them, hope with them; you've got to take on their world's existential real; you've got to forget that these are written words and let them absorb you.
Thou turnest man to destruction; * again thou sayest, Come again, ye children of men.
For a thousand years in thy sight are but as yesterday, when it is past, * and as a watch in the night. (link)
And in these characters' despair, in the dark you'll share with them, we're going to look for some hope. It's there: sometimes, you have to prize not the lost vase, but the surviving shards.
(And if you're really keen, maybe read the movie's script. Such oddness, to me, that a movie can exist in paper form, though of course it doesn't really.)