short answer:
No, and probably never. For password hashing, BCrypt & PBKDF2-HMAC-xxx are better choices than any simple SHA-1/2/3 algorithm. And until SHA-1/2 actual have feasible preimage attacks published, SHA-3 is actually the worst choice, specifically because of it's speed and low cache footprint.
longer answer:
A major factor in the relative security of different password hashing algorithms is: how much faster can a dedicated attacker hash passwords compared to you? That is, how much faster is their software/hardware combination (purchased for the express purpose of password hashing), versus your software on your server (off-the-shelf C implementation for software, hardware purchased for the needs of your application).
One of the main SHA-3 criteria was that is should run efficiently on embedded architectures, which are typified by small amounts of on-die cache, registers, etc. But this also describes modern GPUs: fewer registers/accumulators, smaller on-die caches; but on the flipside, their silicon is optimized to perform the same task in parallel on LARGE amounts of data. This is perfect for your attacker's brute-force attempts: for ever dollar spent on silicon, your attacker gets more SHA3 hashes/sec by buying another GPU than you do by buying a better CPU.
For this specific reason, BCrypt was designed to do a larger number of reads/writes to an in-memory table, one that's currently larger than the cache of most GPUs. Which means the current GPU-based BCrypt implementations aren't even up to speed with their CPU counterparts. So just by choosing BCrypt, you've slowed down your attacker's advantage for every dollar he spends, by forcing him to buy CPUs the same as you.
This is why raw speed is the enemy of password hashing. You want to choose the algorithm whose fastest software/hardware combination offers your attacker the least advantage per dollar over the commodity software/hardware that you'll be using. Right now, that's BCrypt, or the slightly lesser choice of PBKDF2-HMAC-xxx. Since GPUs are probably only going to getter better at doing SHA3, I doubt it'll ever be the correct choice. I don't have the numbers on SHA3, but "which is more secure" is not a nebulously relative term - the above rule can be used to precisely quantify it.