Not to state the obvious, but Mark Millar is typically a great "ideas guy" but kind of a terrible storyteller. He also has a penchant for being mean to both his characters and his audience alike, since being an edgelord got him plenty of attention over the years. (Garth Ennis is far better at that sort of thing, but whatever.)
So really, the fact that both the Kick-Ass and Kingsmen movies are better than the books is to be expected. I say this as a guy who really loves Old Man Logan... up until the last chapter, anyway. Man, is that final curtain draw a disappointment.
If anyone has an argument for 300 being better as a comic rather than as a film, I'm all ears. Zack Snyder isn't perfect, but what he is good at is breathtaking.
I don't love the Starship Troopers novel, but I adore the smarmy parody that Paul Verhoeven made out of it. I totally understand why Heinlein fans hate the flick, but man, if I had to pick one version it'd be no contest.
I won't get into a fight with any hardcore Stephen King fans - I was one myself once, after all - but Stanley Kubrick's The Shining is a masterpiece of a book that's all over the place. That said, King clearly wrote the book in part about his own struggles with addiction, so I can kind of understand why he hates the film, even if it's a hundred times better than the shitty miniseries adaptation King approved of years later.
Park Chan-Wook's revenge film Oldboy is, technically, based on a manga. Everything that makes the film iconic, however - the hallway fight, the sushi bar scene, the way Choi Min-Sik is unable to relate to the world around him, and the big twist - were entirely Chan-Wook's idea. The only similarity between the two are "A guy gets locked in a hotel foom for 15 years, gets released to find out why". That's about it.
I won't claim it's "better", exactly, but Mamoru Oshii's film version of Ghost in the Shell bears so little resemblance to Masamune Shirow's original books that they're entirely different characters and stories with a few common elements.
I adore the Shigurui manga, but my regret is that the TV series ended at 12 episodes because the pacing, art direction and deconstruction of the fighting styles was improved over the books, which were already fantastic. The character development and theming behind Gantz feels a lot more natural and sensible in the TV series, though in doing so they skip the dialogue that actually explains the friggin' plot, so... six of one, half-dozen of the other I guess.
...does Darren Aronofsky's Noah count?
Edit: The Berserk TV show is fantastic in its own right, particularly the score and Japanese cast. It's just not as good as the manga, which is a hell of a tall order to top.
The new CG trilogy, on the other hand...