I’m not going to focus on any plot or sequence changes between the Tekkonkinkreet manga and the anime. I generally felt that the storyboarding decisions made by Studio 4°C were very successful in distilling the manga into an entertaining film. I’m more interested in a few more expansive thematic and aesthetic changes.
Taiyo Matsumoto’s representations of the two boys make them look like little goblins most of the time. They’re all teeth, bandages and runny noses.
One thing that really stands out for me about the anime is that Black and White are much cuter and (I think) look more like real children. I can understand Michael Arias impulse to sentimentalize the children. I love both Black and White (as, I think, Arias does) and it doesn’t seem a disservice to make then more appealing and, well, human.
I also appreciated that Arias did not overemphasize the dichotomy between Black and White. There seems to be a tendency in reviews and critical commentary on Tekkonkinkreet to focus on a reductionist body/mind duality between the two characters. Black is often framed as a reactionary, violent thug despite his cunning and the deep well of emotion and thoughtfulness that clearly motivates his actions. “Nebuchadnezzar II built Babylon.”(!?) 
White is usually described as a pacifist idiot savant but there are many points in the narrative where White’s behavior defies that expectation. While the boys do express a symbiotic duality during points in the manga it’s not the sum of their characters. I think a thorough reading of the manga reveals a lot more nuance in the characterization and I appreciate the acknowledgment of that in the anime.
The sequence where Black very literally confronts his darker psychological tendencies is very beautiful in both the manga and the anime. The “psychadelic freak-out” qualities of the scene are reminiscent of many anime where, at the conclusion, a dissolution of conventional narrative is replaced by visual symbolist sequences that, at best, speak directly to the right side of the brain or, at worst, dissolve into unintelligible nonsense. (To list a few other examples of this trope… Akira, Howl’s Moving Castle, Paprika and, perhaps most famously, Neon Genesis Evangelion.)
Without adhering to closely to the manga Arias really does a nice job of translating Matsumoto’s abstractions into a visually lyrical sequence that maintains a sense of narrative as well as appealing to emotional logic.
I think it should be evident by now that I really love both the manga and anime of Tekkonkinkreet. I feel lucky that I read the manga first – it is one of my favs of all time – but the anime illustrates how adaptations can transcend reductionist fidelity. Having read and loved the manga increased my enjoyment of the anime as both a reverent homage and a creative departure from its source material.
 Matsumoto, Taiyo (2007) Tekkonkinreet: Black and White. San Francisco: Viz Media. page. 71, panel 3.
Media: Tekkonkinkreet anime, onsen scene (thanks to thelostroom1880) [copyright 2007 by Sony Pictures]
Images: screen capture from Tekkonkinkreet anime [copyright 2007 by Sony Pictures], panel from Tekkonkinkreet manga [copyright 2007 by Viz Media], more screen captures from Tekkonkinkreet anime [copyright 2007 by Sony Pictures]