Just off the top of my head:
-Susanoo dies during the assassination of Bolic arc, the whole fight between Esdeath and Night Right in episode twenty one more or less happens in that story line, the rescue and subsequent battle to rescue Tatsumi from public execution is entirely different.
-The character Syura and his team Wild Hunt play a significant role...and are utterly reprehensible. They're basically the Jaegers and Night Raid if they had no redeeming qualities.
-Lubbock is captured and brutally tortured by Syura. Both his and Syura's deaths are entirely different.
-Wave actually gets to do cool shit. He got shafted hard in the anime.
-Kurome lives. (Haven't read that far yet since the translation of volume thirteen hasn't been released)
-Tatsumi and Mine become a couple.
-Budo is way tougher.
-Tatsumi becomes much more bitter as the story goes on and starts to fuse with Incursio.
-Esdeath is way more powerful than what was shown in the anime. She's also more brutal than what was shown in the anime too. Still lovable though.
-Run has a character arc and later dies. His personal vendetta was mentioned in the anime, but never delved into.
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Spoiler