The s3 has great battery life. It also has a bigger battery because it is a bigger phone.
As for your Nexus, have you tried another battery? The only way I see your battery losing life while plugged in is through USB. If you're losing while on the wall charger then something is wrong with your battery. Also when on FB and you lose like 10% when on for 3min what are your brightness settings and are you on 4g? Do you happen to have alot of photos on your page or newsfeed?Also, I recall from a few months ago you were overclocked, are you still? Things like these really add up to draining your battery in a short amount of time, though 10% in 3min seems like a battery defect as I don't even lose that much that quickly playing an HD video on YouTube on full brightness.