Both anime have the same theme: the strenght of hummanity and it's power to fight on against all odds. Both also feature a war that humanity is involved into, bittersweet moments and hints of romance; although TTLG is more over the top and comedy centered, in other hand NGNL Zero is a war drama.
Two completely opposite takes on pretty much the same idea of humaity being on the brink of destructionbecause of war with other races. Willstr NGNL0 is more drama focused Gurren Lagann is more comedy, over the top.
What connects these two movies is a story about how fights against all odds for the right to survive in world seemingly trying to make them extinct. No Game No Life: Zero is fantasy story whereas Blame! is a sci-fi story. If you were disappointed by how No Game No Life: Zero did not focus nearly enough on the struggles of humanity (better bleakness, hardship, death, a sense of hopelessness for the characters) in a violent and decaying world then Blame! provides that kind of engaging plot.