Dropbox works well for small files that you need to share with others. However, if you use it to back up large amounts of data ... say >100GB, the experience of using it is very poor. It consumes large amounts of CPU continually. It takes forever to run to completion (literally in some cases, in my case it ran for weeks before I gave up on it). An external hard drive is of comparable cost to Dropbox, and a one-time cost, not something you need to pay for, forever. It runs to completion in 20 minutes. You can keep multiple versions of it in different physical locations. It's conceptually simple with fewer points of failure.

Personally I tried using several different cloud backup solutions, but I gave up on them. A few encrypted external hard drives, updated every month or two in a repeatable way (e.g. a bash script), one at home, one at work ... and backup is a solved problem. Of course, to each their own.

It's cheaper and faster. What's the hassle or inconvenience of a separate drive? If anything, Dropbox is less convenient because it requires installing an application to use it.

The only drawback is that you have to carry it around anywhere you want to access it. A modern external drive is the size of a phone though, so that's hardly a dealbreaker even if you do want to carry it around. Although frankly, cloud storage is much better for filesharing.

A million game devs cry out with their 500GB project backups on their external drive. Good luck Dropboxing that in a way that makes sense.