Which one offers better battery life? Which one is snappier? Is there a way to install stock android on my GS3? I have the verizon variant running latest software if that affects anything
I haven't tried CM on my S3 but I'm willing to bet that it offers both better battery life and snappier performance.
Yes, it's possible to load it on your SCH-i535 - just look in the rooting sub-forum.
Its a toss up on battery life. Touchwiz may be a bit better. But if you get the right kernel (KTkernel is good) on Cyanogenmod with a more conservative governor, battery life will be great.
On my S3 with CM10.2 and stock battery, I was getting maybe 2 hours of screen time over a 17h long day.