The main advantage with a LiPo is power delivery. They typically have higher drain rates with smaller size. However, the latest big name high drain 18650s compare similarly to the high drain LiPos in terms of power delivery. They have the additional advantage of higher energy density meaning they hold more charge in a smaller volume.
The nice thing about LiPos is they are flat which can be ideal for a box mod. There are round LiPos as Breaktru shows in the photo, but they are not as widely available. You can use them if you like with similar advantages.
Probably the biggest advantage is LiPos can be soldered easily. It's possible to solder 18650s and I do it, but I would not recommend anyone attempt it unless you are highly confident in your soldering skills. It's very, very easy to overheat them and damage them. Makers strongly recommend against soldering them, but it is possible to do it. The best thing is to use welded tabs which you can do yourself with a capacitive spot welder or buy them with tabs already installed. They're not widely available with tabs though.
In terms of safety, LiPos rate between the the ICR type (LiCo) and IMR type (LiMn). They are not as safe as IMR cells but safer then ICR cells. You do need some kind of short circuit protection when using them. A short can cause them to ignite. You should also have some kind of over-discharge protection with them. They should not be taken below 3.0V where the big name high drain 18650s can be taken down to 2.5V or even 2.0V for the LG HE2.
A really big consideration with LiPos is they are encased in a thick foil in comparison to a steel tube for a typical round cell. They are highly vulnerable to physical damage. A puncture will invariably cause them to ignite. The being the case, you need to enclose them in a way that protects them physically.
