A ton of my favorite books are being turned into movies lately- it's something of a golden age for science fiction and fantasy television and movies. The quality of the adaptations is extremely varied, though, and while some are fantastic, some leave... something to be desired.
Altered Carbon is somewhat unusual for me in that I watched the show before the movie. While talking about my response to the show with my neighbor, he asked if I'd read the book, and then loaned it to me when I said I hadn't.
First thing first: The main character. The protagonist of the show, Takeshi Kovacs is, not to mince words, a raging asshole. They try to make him out to be a raging asshole with a heart of gold, but it falls short more often than not. In the book he's still hardly a charmer, but he's at least capable of being polite and friendly, and it doesn't mystify me when the side characters react positively to Takeshi. The clear edge here goes to the book.
The side characters in the show, however, easily surpass the side characters in the book. This is to a great extent just a consequence of the greater length of the television format- 10 episodes gives you a lot more room to develop their personalities and backstory than a few hundred pages do. Poe is the winner here- he's (if it's correct to call a sentient hotel he) the standout character of the show. His book equivalent, Hendrix, appears far less often than Poe does and plays a much smaller role.
It feels a little strange to discuss special effects between a book and a show, but they're definitely there. While books have a functionally infinite special effects budget, Richard Morgan is actually fairly sparing with his use of "high budget special effects". There are fewer flying cars and crazy action scenes in the book. The mansion of the Bancroft's is merely located on the coast, instead of atop a colossal Blade Runner-esque tower. The show goes way more all out, which is strange, because books have an effectively infinite special effects budget.
Plot-wise, I'd honestly have to give the two a close score. The murder mystery is a bit more tightly written in the book, but the side plots and character development are better in the show.
In the final running... honestly, the two are pretty much tied. I'd just go with whichever format works better for you. If you're looking for a new show, this'll do great, and likewise with a new book. If you're looking for something that takes less time, choose the book if it'll take you less than 10 hours to read. They're both pretty decent. Not spectacular, but I didn't feel disappointed about either.