When would one use Manhattan distance as opposed to Euclidean distance? I am trying to look for a good argument on why one would use the Manhattan distance over the Euclidean distance in machine learning.

The closest thing I found to a good argument so far is on this MIT lecture.

At 36:15 you can see on the slides the following statement:

"Typically use Euclidean metric; Manhattan may be appropriate if different dimensions are not comparable."

Shortly after, the professor says that, because the number of legs of a reptile varies from 0 to 4 (whereas the other features are binary, only vary from 0 to 1), the "number of legs" feature will end up having a much higher weight if the Euclidean distance is used. Sure enough, that is indeed right. But one would also have that problem if using the Manhattan distance (only that the problem would be slightly mitigated because we don't square the difference like we do on the Euclidean distance).

A better way to solve the above problem would be to normalize the "number of legs" feature so its value will always be between 0 and 1.

Therefore, since there is a better way to solve the problem, it felt like the argument of using the Manhattan distance in this case lacked a stronger point, at least in my opinion.    

Does anyone actually know why and when someone would use Manhattan distance over Euclidean? Can anyone give me an example in which using the Manhattan distance would yield better results?
According to this interesting paper, Manhattan distance (L1 norm) may be preferable to Euclidean distance (L2 norm) for the case of high dimensional data.
The authors of the paper even go a step further and suggest to use Lk norm distances, with a fractional value of k, for very high dimensional data in order to improve the results of distance-based algorithms, like clustering.