GoKawiilThe primary advantage of external SSDs is their speed. All SSDs use flash storage, which allows random sections to be loaded instantly. For an internal drive, using one of the best SSDs means your system disk boots the operating system and opens apps quickly. On an external drive, the speed boost is mainly applicable when transferring and opening files.
How much this matters depends on how you use the device. If you move gigabytes of files between devices daily, or if you regularly load photos and videos from an external drive to edit, it makes a huge difference. If you want to create an archive of files and then rarely touch it, the speed boosts aren't as important.
SSDs are also more suitable for carrying around. Because they have no moving parts inside, they aren't terribly susceptible to bumps and drops. If you're clumsy or often carry a drive around outside, an SSD will likely last longer. Their simpler internal makeup also makes them lighter and smaller, which is a consideration if you're keeping them in your backpack or bag.
External SSDs don't make noise, which people around you will appreciate. The lack of internal motors also means SSDs require less power to run than a traditional hard drive, which is a factor if you often use your laptop away from a charger and don't want to purchase a laptop power bank.
For all these perks, the largest drawback of SSDs is their cost per gigabyte. Even when storage prices aren't inflated, the best external SSDs provide far less space for the money than an HDD. For example, at the time of writing, Amazon has the Samsung T9 Portable SSD 1TB for around $232, while the Seagate 2TB Portable Hard Drive is $130. Of course, there are various standards and configurations for each, but you're going to get less space for the money with an SSD no matter what.