The Google Nexus 5 comes from the same makes of the LG G2, and the similarities are present. However the LG G2 takes a slight edge with its more pleasing design to its slightly superior performance in various key areas.
However the software on either device will make the decision between the two harder, with Android 4.4 KitKat on the Nexus 5 going up against the heavily customized Android 4.2 Jelly Bean software experience on the G2. With the Nexus 5, you get an unsubsidized device priced at a hard-to-beat $349 compared to the LG G2 which costs around $99 on contract or $525 with unsubsidized.
You can read a detailed comparison between the Google Nexus 5 and the LG G2 on PhoneArena.