The original manga is short and leaves out much-needed character development and detail that the anime adds to the mix. Consider that it's a 3 volume source manga converted to a 26 episode TV series. In this case, it works, and the additions are nothing but positive.

i was an Attack on Titan manga fangirl since chapter 1, but the anime improves on the original thanks to the action sequences, as well as the color/character designs. The manga's artwork is rather sketchy and crude, and it's nearly impossible to tell most of the characters apart... so even having hair color in the anime was a big step up. 

Anyone who's read the Usagi Drop manga will know what I'm talking about. The anime chooses to not adapt the last part of the manga, which is universally considered to be disturbing and gross. 

I'm not sure if others agree with me on this, but I preferred the Deadman Wonderland manga because it focused almost entirely on the gory death game aspect of the prison (which imo was the best part of the manga too). Whereas the manga goes full-on boring shounen after some of the initial vols, with multi-chapter, drawn-out and boring fights and other uninteresting crap.

The anime is far superior to the manga in this case - the cinematography, music, and overall appearance help make the source material far more desolate, unnerving, and stunning.