Possible there's some interference that the LG G3 is more sensitive to than your other equipment is. To find the best setup I use WiFi Overview 360. An excellent tool, it's the best WiFi analyzer I've found. The free version is probably all you need but the Pro version is cheap. The Google Fiber guys use it to setup WiFi when doing installations.
https://forums.androidcentral.com/e?...token=4pW9m_9g
Gve the 5GHz and 2.4 GHz bands a different SSID. When setting up the 5GHz band set the router to use a channel well over 100. Over 150 if there's a clear channel. Of course for both bands use channels with the least interference and best signal. If interference is the problem I doubt that the encryption matters, but you could try AES and WPA2 and see if I'm wrong.
Also, try turning off the 'Automatic' setting in WiFi settings and see if one band is noticeably better than the other. Of course, if interference doesn't muck up the results, 5GHz should be considerably faster, 2.4GHz should carry farther and penetrate walls better.
Oh yeah, I assume that the G3 WiFi works correctly when connected to other networks, yes?
Android since v1.0. Linux user since 2001.