The batteries in the 787 are lithium-cobalt-oxide, which apparently at the time were the best available. LiPos have more energy, and can handle more cranking power, but have a fairly short life (~500 cycles?). Electric cars nowdays have lithuim-iron-phosphate (LiFePO4) batteries, which have less energy than LiPo but a much longer life (~5000 cycles). I suppose for an aircraft it's a matter of trading off more power for the weight, or longer life.
Still waiting for lithium-air cells!