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According to every source I've found the only advantage of Li-Po is their shape, but they are more expensive, have lower energy density and are more dangerous compared to Li-Ion.
Why do drones use Li-Po batteries instead of Li-Ion batteries for example 3s2p 18650 Li-Ion with 40A protection circuit.
For this answer I'm going to define LiPo as flat packs, and Li-Ions as 18650s. The reality is more messy than that, but I believe this way of defining the terms will help answer your question as you seem to have intended it.
Traditionally, 18650s didn't support high current applications, a continuous current rating of 5A was considered to be high. 18650s that support 20A continuous current were more or less unheard of until high power cells like the Sony VTC3 came on the market.
(As a general rule, 18650s that claim to support more than 30A continuous, even today, are simply overrated. There is also a trade-off between capacity and continuous current capability; For example the 30A Sony VTC4 is "only" 2100 mAh.)
A lot of the reason why drones use lipos are probably tradition, due to this.
When you say that LiPos have a lower energy density, you mean a lower energy to volume ratio, right? I'm pretty sure they have a higher or at least as high energy to weight ratio, as Li-Ions. 18650 Li-Ions have a metal casing. That's unneccesary weight.
The flat form factor of many LiPos probably also helps with cooling.
Weight and size also play a role. LiPo packs don't use a metal housing (=less weight) and the way they are build makes that use a lot less space compared to 18650 cells.
the reason why people don't use 18650 as power source for drone is the C rate problem or discharging current.
for most 18650 battery packs, a 5C rate is sometimes hard to reach for most of the small manufacturers in china not to say 10C or 20C(technology is a problem, pricing is another problem, if more chinese companies can make batteries that reach 20C, pricing should be lower.)
but things are quite different for lipo batteries, 30C is common for most of the manufacturers
so again, lipo are more cheap and mature for high rate discharging applications.
we can't use Li-ion for drones. at least i have tested 2 18650's 5800mAh in parallel: when you connect these to motors without board batteries get hot very soon and the speed of motors come down. but via a Li-poly motors work really better.
discharge is no problem AT ALL. sanyo L ncR 20700b 6612 Li-ion cells have a 15c discharge, & parallell 4x, you get 60c. this practice is not uncommon in Lipo batteries either. and NO- the problem is not size vs. watt hours. the power density of a 20700 is almost double that of the most powerful Lipo, including the case. the only comparison that matters is power to weight density. and for 20700's this is 106wh per Lb. if you want to see how that stacks up against Lipo, look online at the battery weights/specs & do the math. you'll discover that Lipo is about 60wh per Lb... BUT- you have to build your own pack and brave the risk of no discharge protection (unless you know someone who can custom build the circuit for you).
