Welcome to Android Central! As you probably know, both phones are fast and powerful. Here's my breakdown of the pluses and minuses.
Nexus 5
+ pure Android, no bloat
+ first in line for system updates from Google
+ more likely to be supported with updates for longer than the G2
+ very good camera (from my experience)
- mediocre battery (expect about 3 hours of total screen-on time)
- mediocre speaker (mono)
G2
+ much better battery
+ many feel the screen is better
+ even better camera, more MP
+/- button location not for everyone
- LG skin a little too busy for me, also has bloatware
If you're not looking for a total workhorse, go for the Nexus 5. If you plan on using your phone pretty heavily through the day, though, you'd end up having to recharge the N5 at least once, so the G2 might be a better choice.