I've been setting my G3 up the way I want it since late thursday. My phone spent most of the evening downloading all my apps, and REALLY drained my battery fast since I was on 4G. I left the office at 5pm with a 96% charge, and by 7:30pm I was down to 34%, which I found shocking.
Friday I was using it at the office for e-mail, SMS, and several phone calls, and didn't really tax it that hard. Battery drain, relative to my S3 was still much greater.
Yesterday I set up Apex launcher the way I had my S3, and still noted substantial battery drain on my new G3 relative to my old S3, and that continues to be the one thing that I have major concerns about my new G3.
The G3 is relatively fast in most areas, but compared to my S3, I expected it to be a little more zippy.
I really like the size of the screen combined with the efficiently sized form factor. I like the screen, and while the brightness is quite subjective, I've set mine up to 70% (probably why my battery is draining out so badly), and it's very satisfactory to me at that level. The screen on the G3 blows the S3 away easily. The G3 came pre-set at 39% brightness, which was too dim. It was rainy here yesterday, and will be cloudy again today, so I haven't had it in direct sunlight to compare to my S3.
Today I'll use my phone to take notes with a bluetooth foldable keyboard while I'm at church, and will observe battery drain compared to my S3. My S3 will usually drain about 15-18% points per hour, and I suspect my G3 will be more.
I'll post additional observations later, and hope this helps S3 users think through both pros and cons while considering the G3.