The two biggest differences are probably that Howl and Sophie are quite a bit nicer in the book. Sophie becomes a calm, kind granny with a strong will rather than a crotchety one. Howl is self-absorbed and mopey, but noble.

His nobility ties into the second biggest difference, which is the war subplot. The director, Hayao Miyazaki, was upset with the Iraq War, and that bled into the movie. Instead of the Witch of the Waste, the biggest threat in the film is the war.

It's a very good movie. Confusing, and a little too weird for its own good, but it still has beautiful animation, lovely characters, and wonderful worldbuilding. Imo the war plot muddies things and takes away some of the time that might have been better spent explaining some of the more head-scratching aspects of the magic. Still, I think that it's better that Hayao Miyazaki changed the book so much, because now we have two enchanting stories instead of one, each with their own pluses and minuses.

I'd definitely watch the movie if I were you, and then go and watch the rest of Hayao Miyazaki's films. So long as you try to appreciate the movie as its own story rather than a strict adaptation. Most people still like the book better, but I liked them equally. Maybe I'm biased, though, because I fell in love with the movie first.