That's... debatable. I personally found the anime handled a lot of things better. Don't get me wrong, the manga is pretty damn solid, but it dervies most of its tension from the dissonance between the moe highschool club anime it pretends to be and Gakkou Gurashi and it plays that latter part a lot stronger. There's a lot less of the vaguely underlying sense of hope the anime had at times, too.

By contrast, the anime bottles up a great deal of tension priarily through two things: completely unsubtle foreshadowing and deathflag raising, to the point where characters will almost literally say what is going to happen several episodes in advance, and dragging out the big reveals to an almost excrutiating degree whilst dropping hints that something is amiss the whole time. The end of the first episode is a great example of that. The manga makes the same reveal after less than 20 pages of the 170ish page first volume, and it's nowhere near as effective for it. It's also way, way less subtle about Gakkou Gurashi something it likewise reveals in the first volume.

I'd still say it's worth a read. Whether anything I mentioned bothers you is going to depend on your own personal tastes, and there's a lot of pretty good shit that was cut out of the anime for one reason or another. The post-anime-content storyline is pretty good too, though I have to admit the new characters are kinda down the list of things I find interesting and/or desperately want the story to expand on, and they're currently hogging up a lot of the attention.