Im Not sure why there are lines with the 6770m but not with the intel Hd Grphics Please help me With This
Do you have anti-aliasing enabled? Minecraft looks like that on my system if I force Anti-aliasing (or was it anisotropic filtering? Can't remember...try disabling both to see if it helps)
I see some dark pixelated sections on your Intel side also. Settings or drivers most likely. Unless you have a heat issue.