As the author of Sandstorm, I'm going to say: "ehh... maybe."
There's still some big differences between Sandstorm and Docker's sandboxes -- not as big as there used to be, but non-trivial. For example, Docker mounts /proc, albeit read-only; Sandstorm doesn't mount it at all. Docker lets the container talk to the network; Sandstorm gives it only a loopback device and forces all external communication through one inherited socket speaking Cap'n Proto. In general, Sandstorm is willing to break more things to reduce attack surface; Docker puts more priority on compatibility.
So is it "secure"? That's not a yes/no question. Security is about risk management; you can always reduce your risk further by jumping through more hoops. There will certainly be more container breakout bugs found in the future, including bugs affecting Docker and affecting Sandstorm. There will probably be more that affect Docker, because its attack surface is larger.
There will also be VM breakouts. VM breakouts appear to be less common than container breakouts, but not by as much as some people seem to think. Anyone who makes a blanket statement that VMs are secure and Docker is not does not know what they are talking about.
The only thing I'd feel comfortable saying is "totally secure" is a computer that is physically unable to receive or transmit information (airgapped, no microphone/speaker, etc.), but that's hardly useful.
In general, if you are going to run possibly-malicious code, the better way to reduce your risk is not to use a better sandbox, but to use multiple layered sandboxes. The effect is multiplicative: now the attacker must simultaneously obtain zero-days in both layers. For example, Google Chrome employs the V8 sandbox as well as a secondary container-based sandbox.
In Sandstorm's case, the "second layer" is that application packages are signed with the UI presenting to you the signer's public identity (e.g. Github profile) at install time, and the fact that most people only let relatively trustworthy users install apps on their Sandstorm servers. (For Sandstorm Oasis, the cloud version that anyone can sign up to, application code runs on physically separate machines from storage and other trusted code, for a different kind of second layer.)