Naturally, the book is much better and is also vastly different.
The most obvious is that the main themes are almost the same, but whereas in the movie the humanity of the androids and actual humans gets somewhat blurred, in the book there is a very clear difference between the two. Androids lack empathy, although they are incredibly good at concealing it. This is, in fact, why Deckard struggles with his humanity--not because he can't tell whether or not he is real, but because his occupation as a bounty hunter is such a contradiction. As a human he is endowed with empathy, but killing (or "retiring") androids requires that he ignores it. Even though the word they use for it is different, it's pretty clear throughout that he thinks of himself as a murderer.
This is also one of the points where I think they simplified and screwed up the plot in the movie because whereas the film features a romance subplot between Deckard and Rachel Rosen the android, the book never really goes that far. At best, he develops a crush on her that is mostly based on lust. It's rather important, I think that he doesn't completely identify with her yet, but is certainly beginning to, and it worries him. A colleague, another bounty hunter who is far more cynical than Deckard, points this out to him by explaining that he's thinking about Rachel backwards--he needs to have sex with her first and then kill her, which he does, later on, and then feels rotten for it.
I also hadn't realized when I started the book that the title is much more literal than I had thought. Because of the whole empathy difference between humans and androids, most humans are required to tend animals, the reason being that an android would not be able to identify with the creature and would let it die. But since the whole thing is set in a post-apocalyptic world that's been ravaged by war, most animals have gone extinct. The few remaining are highly expensive and there is a large trade in fake electric replacements as a result. Deckard has one of these and expresses a lot of jealousy throughout towards those who are able to afford their own real animals. Towards the end of the book, several of the androids end up being very cruel to a few of the real animals due to their complete lack of feeling towards them, and I have to admit that, unlike in the film, it made me stop feeling at all sympathetic towards them. Maybe it's because I hate animal cruelty so very much, but I wasn't feeling the "pro-android" vibe that was pushed in the film so heavily. I think part of that was intentional, in fact.
There's a whole lot of other stuff going on in the book as well, but that's all I feel like touching on at the moment. It's way more nuanced than a film adaptation could ever be, and if you're into science fiction at all, I'd definitely recommend it.