Given the battery technologies your civilization uses, bullets are clear winners. It's all in the energy density.
Wikipedia has a convenient table of the energy densities of all batteries. The 3 battery types (2 are subsets of lithium-ion) you've listed, Lithium-sulfur, Lithium-polymer, and Nickel-cadmium have energy densities (by weight in MJ/Kg) of 1.07, 0.7, and 0.11, respectively. For comparison the energy density of gunpowder is 4.7, body fat is 9.74, gasoline is 13.3, and ammonia is 16.9 (all including the weight of the oxygen) . We'll assume the batteries will be used to fire lasers, and that the chemicals will be used to launch bullets. Lasers are a pretty good way to turn battery power into destructive energy, and chemicals can release their energy explosively when sufficiently mixed with liquid oxygen.
Now, we must consider the different weapons technologies. Let's start with the chemicals first. Using Zeiss Ikon's value of let's call it 500J per bullet, and assuming a 32% efficiency for small firearms, 100g of the chemicals will launch:
- Gunpowder: 300 rounds
- Body fat: 623 rounds
- Gasoline: 851 rounds
- Ammonia: 1081 rounds!
And for batteries, assuming a 50% efficiency for lasers:
- Lithium sulfur: 107 blasts
- Lithium-polymer: 70 blasts
- Nickel-Cadmium: 11 blasts.
And that's ignoring the fact that most energy from a laser pulse goes into surface heating, instead of penetration and tearing which is far more damaging to living beings, as well as the fact that batteries are not meant for such quick discharges. It's hard to know for sure, but some estimates from the internet suggest an energy of ~1MJ to do similar damage as a bullet. If that's true, none of your batteries will be able to produce even one blast! (Never mind the fact that with a mirror, more than 90% of the energy can be deflected away, requiring at least 10MJ to do serious damage)
So unless your civilization really steps up their battery game, modern day tech has no chance against actual bullets. And even if they could, bullets do a lot more damage with impacts than the localized heating of a laser, making them a better technology for destruction.