Except RAM, there is no reason to pick 820. I was excited to pick 720 but lack of proper RAM made me suspicious. Nokia could have charged a little more and given proper RAM on 720.
-> Camera - 720 wins because of low-light optimization
-> Battery life - 720 wins because of bigger battery
-> Display - 720 wins because it has an IPS LCD vs AMOLED. IPS wins any day of the week.
-> Weight and Design - 720 wins because its lighter and much better design.
-> Processor - 720 wins because it's newer generation as opposed to 1 year old on 820. Also 720 has Adreno 305 vs Adreno 225
If 720 had proper 1 GB RAM, I would have bought it in an instant. Now I will wait!