And beyond just being a subset of the features, it doesn't have Dropbox's ecosystem. Can you auto-sync your Oreilly Media books automatically with own cloud right from the Oreilly website? Does 1Password automatically sync with it? Is there a screen sharing app that automatically pushes to owncloud? Does it have a push API? IFTTT support? I, and others, use all these with Dropbox and it probably doesn't make sense to give them up because the NSA is the boogeyman FUD.
As you mention, hosting OwnCloud removes your cat/fire scenario. Even by hosting it at a US ISP, you are significantly reducing the likelihood that the government can index or be two clicks away from your data, and your host (unlike Google/Dropbox) isn't likely to be mining your data for future business models. Hosting it at an ISP in a country that respects individuals privacy (e.g. Iceland) means your data won't be in the government's hands unless you're directly targeted by a state actor.
A subset of the features is, for me, an advantage. Hosting my password database myself is a huge feature. My Mac's built in screen capture writes stuff to disk. I can set that to be the Owncloud folder. No third party app required! :)
You don't have to write your own Dropbox. You just have to host one.
And even beside the question of government surveillance there is the advantage that it is under your control, not somebody else's. File sharing is so generic that the lockin opportunity is less than it is in other domains (like social networking) but there still can be advantage to being the owner and not merely a renter.