I think it all depends on what you use your phone for. If you want a great web browsing experience and good movie watching/ebook reading comfort, go with the Note 3.
If you use a phone only for calls and texts, with only occasional media consumption, go with the G2.
I had the G2 for a long weekend and decided to return it and wait for the n3; I watch a lot of movies and shows during my lunch hour and early morning before anyone gets in the office, and while I enjoyed the G2's gorgeous, super bright display, I kept thinking that the screen could be bigger.
I've got a bad feeling about this.