A Ni-Cad battery of similar size and weight is capable of starting a heavier APU for the 777.
I was watching a TV program the other day that mentioned Li-Ion batteries and it suggested that Ni-Cads of similar performance would be six times larger/heavier. I took it with a pinch of salt but you never know.
Bearing in mind that Boeing removed the original access door from the forward hold to the forward electrical bay and replaced it with a fixed panel just to save weight gives you an idea of how weight critical they are.
If the Li-Ion Battery is half the equivelant weight or more of a Ni-Cad......