ok i just watch the video
That video didn't prove a thing other than that the phones perform at very similar levels. The only real difference in performance I saw was that the note 3 did a much better job with google earth. As the g2 zoomed in it kept skipping where the note 3 zoomed in smoother. These kind of internet speed comparison test are not scientific in the sense that they are too many variables at play which could effect results. (you might be thinking that that wasn't an internet speed comparison but an app opening comparison but I beg to differ when almost everything he opened relied on an internet connection. I could really thoroughly pick that, and similar videos apart for their tremendous lack of scientific methods) For instance where is the wifi signal coming from. Is it equal distance from each phone? Or perhaps it might be on the side of one phone or the other. Also you are dealing with wireless signals which move a lot and are not the most consistent things, and where is a live data bit speed calculator showing how much data each phone is being sent by the wifi signal. You might find that the wifi is sending one device more information than the other due to multiple variables. If that video makes you make your decision on which phone is better then that's sad because I basically learned nothing from watching it. to each his own...
Advice - compare each yourself and decide which you like more, this isn't a contest people.
And to answer the Ops question. If it is faster, that may be due to 4.3 or it could also be because of software optimizations within samsungs rom itself. From reports and reviews i've seen on the g2 there does seem to be some software issues with it. i'm sure we'll see some huge updates for the g2 over the next 6 months