I'm not sure why you posted this, I didn't make any mention of size, weight, or efficiency. Still, to expand -
Grid storage is indeed not very concerned with size(volume, weight), but are interested in overall cost and efficiency. Everything I've read has LiIon being not just top of the line for energy density, but also comes out high for energy efficiency - this is where lead-acid tends to fall down. It's energy efficiency tends to be about equal to the Nickel chemistries - NiCad and NiMH.
I mentioned the price because LiIon has been becoming cheaper per joule per years, when the nickel in NiCad batteries has been increasing in price, driving up the cost of battery chemistries that use it. NiCad is still cheaper, but for how long? Musk is planning on chopping the cost of LiIon in half again with this factory.
The BESS ended up being $5 per watt-hour, but it's a complete UPS system. We don't know how much the batteries/chargers were specifically and how much was the facility and AC generation equipment.