The G6 has a significantly better GPU. It is a dedicated AMD Radeon instead of the Envy 15's Intel HD graphics.
What's the price difference? I would choose the G6-2236TX just because of the GPU alone. The G6 also has a quad core i7 CPU instead of a dual-core i5 CPU. The CPU in the G6 has a passmark rating of about 7000 while the Envy 15 has about 4500.
The G6 is definitely better.
Good luck!