A lot of the author's estimates are on the higher side, which takes him to the ~10^21 number. Fair enough. But even then one must concede that, say, a rat brain, with 1000 times fewer neurons, should still be within reach of modern supercomputers in terms of sheer processing power.

And even the authors of both those posts note that biological brains are VERY different from ANNs, which could confer them significant advantages. That is my own view - the biological brain is just better at what it does, and our algorithms will require significant changes to match that level of efficiency. Of course, we still need significant advances at the hardware level as well (the human brain barely uses 30W and still has some 3-6 orders of magnitude more computing power than the most powerful GPUs that easily use ten times that much power), but even with such advances we may not be able to match the biological brain unless we make some more fundamental changes to our methods.