Polymer batteries vs Lithium-ion batteries 

Essential difference

 In fact, they are "relatives". Lithium-ion batteries use liquid electrolyte, while polymer batteries replace the electrolyte with gel or solid form, just like changing water to jelly.

Safety

This is the most practical advantage of polymer batteries. Ordinary lithium-ion batteries may catch fire and explode if overcharged or bumped, while polymer batteries will only bulge at most and will not explode. They are much safer. 

Light and flexible

Polymer batteries, due to their lack of a hard casing, can be made as thin as a bank card. Their shapes can also be customized at will. This is why nowadays, as mobile phones get thinner and thinner, it is all thanks to them. And at the same capacity, they are much lighter than lithium-ion batteries.

The drawbacks are also obvious

expensive! Polymer batteries have high costs and their cycle life is generally not as good as that of high-quality lithium-ion batteries.

Summary in one sentence

If you value safety and portability, choose polymer; if your budget is limited and you want durability, go for lithium-ion. There is no absolute superiority; it all depends on where you use it.