This video comparison was very useful for me- specially the ending bits- the camera quality. Interestingly, GSMArena crowned Note 3 putting G2 in 3rd position in Low Light>Flash On condition
thanks to Note 3's powerful Flash. Your video reflected that too.
It was seen Note 3 has done better job than G2 in that condition
And I also agree that G2 being slightly snappier than Note 3.
Phone: Sir Galaxy S To The 3rd
Variant: I9300GT Pebble Blue 16 GB
ROM: JB 4.3 | XXUGMJ9 Baseband
Recovery: PhilZ 5.18.5 | CWM 18.104.22.168