I’m already hearing that the Z3 is not a go for many because of the lack of a 2K display.
So let’s compare the two.

The Xperia Z3 has a clear and bright 5.2-inch 1080p LCD screen with a pixel density of 442ppi and Sony’s TRILUMINOS Display, Live Color LED, and X-Reality and the LG G3’s 5.5-inch QHD display with a pixel density of 538 ppi is amazing BUT. While the increase in resolution is noticeable, the G3’s has a dim display, color inaccuracy, and its clearly over-sharpened when you hold them side by side. Both phones are amazing  to look at. But in my opinion the Xperia Z3 is the winner.
As 1440p games and video become available for the G3 then I would possibly change my mind. But as of now everything is still 1080p unless you are watching a TK Tech News video in 1440 or MKBHD in 1440 on YouTube, there really isn’t a use for 1440p displays at this time.