i had a black g2 a few days ago, i traded it with nexus 5, used te nexus about 2 or 3 days.
the battery life is a real difference that you wil notice (im a heavy user) .. the camera yes is somehow seems old to me.
performance: i didnt find a major difference. the great RAM management of the nexus is better but i didn't feel the g2 slower or something. of corse vanilla android is a familiar experience and has its pros
in hand: the nexus make you a little bit confident, better grip due to the Mat back. really confartble to use , especially with one hand. the nexus is way confertable in hand.
by the way, ive sold the nexus Yesterday cz i couldnt resist the offer ($)..i had money in hand and wanted to buy a new phone. head to the store, saw the htc M8, Htc M7, samsung S5, htc one max, note 3, xperia z2......many many phones in store......... i looked at the LG part, saw a white G2.. absolutly irresistible !! took it and payd the guy...went home... got internet..updated the g2 to 4.4.2....rooted it... ignored the 18 months warranty card hehehe.... xposed framework..& VrooOoooMmm VrOOooMmmM ...felt the same feelings when cruising in my '79 Pontiac Trans Am Muhuhahaha