Generic is a "catch-all" build for x86 (Intel/AMD) CPU systems. OpenELEC 6.0.3 releases are available in 64-bit (x86_64) formats only whilst legacy builds (v5.0.8 and earlier) are available as both 64-bit (x86_64) and 32-bit (i386). Unless you have 32-bit hardware, use a 64-bit build (x86_64).
The nVidia driver in the OpenELEC 6.0 build does not support older nVidia GPU's including the popular ION (GeForce 9400m) card. If you have an nVidia GPU and see a message about unsupported GPU's after installing or updating to OpenELEC 6.0 please change to the Nvidia_Legacy build.