> > run the various computers
>
> That's a vague assertion that can apply to anything.
It's a very specific assertion which does not apply to every thing: with syncthing, you need to operate every piece of the system. With a cloud service, you are delegating that to other people, presumably professionals. That's a big difference for most people and it has significant implications for things like backups — e.g. if someone breaks into your house and steals two computers, did you just lose every copy of your data?
> > provision enough storage to hold everything
>
> Syncthing can ignore directories/patterns at the local level.
That's an unrelated topic. This is about the total size of your data and whether it fits on multiple devices without inconvenience. If you have a phone and a laptop, do you have enough storage for a full copy of everything? If not, you need to add a third computer, deal with external drives, etc. One appeal of cloud services for many people is that you can save your data without needing to have enough space to have a full local copy and still be able to access it.
> > secure them
>
> And this notion somehow doesn't apply to your Dropbox credentials or shared folders? Furthermore, Dropbox has access to your data - with Syncthing that's limited only to the synchronized devices.
Again, this is a comparison question. A service has a separate security trust boundary so someone who compromises your account doesn't get infrastructure-level access and cannot permanently delete things without you having a chance to recover. If you're doing it yourself, you're taking on that responsibility entirely yourself. Maybe you're confident with that, maybe you're not but it's something that you absolutely have to think about for a data storage system.
> > have a backup plan
>
> Another non-sequitur. Either tool can be part of a backup solution.
You might want to check the definition of non-sequitur – it's not a get-out-of-jail-free card for avoiding an answer. Just to reiterate, ask what happens if your hard drive starts corrupting blocks, someone steals your computer, your house burns down, you get malware which encrypts every file on your computer, etc. With Dropbox the answer is “I buy a new computer and restore my data. Since the malware couldn't overwrite the older copies, I lost nothing”. If you're self-hosting, that could have the same answer but it requires more skills and ongoing commitment to do things like off-site backups.
What I've found to be sadly common is that people do these comparisons without actually matching equivalent levels of service and then get a painful educational lesson when something goes wrong and they lose something they cared about.