no battery has 100% efficiency. 
like i said, 2.5 times for note 2 is about right.
remember, note 2 is 3000mah capacity. direct division will never work with batteries.
power could be affected by cable efficiency, battery efficiency and loss as heat.

anything big. yb642 and above. if u dont mind size, get the yb665.
it all depends on user preference. i can recommend the best, but if u gona complaint about the price and the form factor then kinda defeat the purpose aint it

i dont have note 2 sorry. but its as big as note2 in width, a little taller and 2.5 times thicker than note 2