A lot of things were different toward the end of the anime because the manga hadn't been finished yet. My guess is that they share certain similarities because Nakayama/Ditama shared what they had thought up so far with Gainax, and the anime and manga both went on based on those ideas.
In the anime it seemed to be insinuated that Slash died shortly after the massacre where he killed the Keepers. I'm not sure about the manga.
And, finally, I have to say that I liked the anime's version of the story better. The manga seemed to be mainly based around the idea: "take every single American conspiracy theory (Area 51, JFK assassination, Keepers, psychic abilities, etc.) and make them into a maid story." It worked very well, but the anime toned down the conspiracy theory concepts, removing elements of Area 51 and psychic abilities all together, and episode 10, none of which was in the manga, was probably my favorite episode of season one. Overall, as ANN's review said, the anime's a better story; the manga's a more complete story.