more powerful in the statistical sense? I though non-parametric tests were usually less powerful than those where a certain distribution is assumed.

You would be surprised what number of samples does to the tests. Take t-test -- the most powerful test to check if means of 2 equivariant Gaussians differ. If you compare the asymptotic efficiency of Mann-Whiney (a distribution free test) relative to t-test is around 0.96. Of course in practice you will not have infinite samples. It then comes down when do these asymptotics kick in. Unfortunately that depends on the distribution.

That depends on whether the assumed error distribution is accurate. Obviously, if the distribution is known, you will do better by incorporating it. But assuming Gaussian errors when the data doesn't match can lead to bad analyses.