In my view, nominal GDP targeting is superior to a price level target when there is a decrease in the supply of some particular good (the cotton blight.) It is also better when there is a shift in demand, and the prices (including resources like wages) are sticky in the sector losing demand.
Are there any scenarios where a price level target is superior to a nominal GDP target?
Suppose there is a 10 good economy. All goods are produced by self-employed sole proprietors. There is a uniform reduction in supply for all goods. Perhaps the economy is all agricultural and there is bad weather. More plausibly, there is a government regulation that has more or less the same adverse effect on all economic activity.
While the decrease in supply of each and every good would seem to raise their prices, the reduction in the real income that can be earned will reduce the demands for each and every good. If prices remain the same, all markets clear. The price level is the same. With the quantity of each and every good reduced, real output has fallen. Lower quantities at constant prices implies less expenditure on output. This results in a lower nominal income. Lower nominal income at constant prices is lower real income, matching the lower real output.
If one of the 10 goods serves as medium of account, and its supply is reduced in proportion to all the other goods, then the result is as above. On the other hand, if there is a fiat currency in fixed supply, (or a gold standard where the existing stock of gold is taken as fixed,) and money is a normal good, then the reduction of real income will result in a lower real demand for money. Given the quantity of money, there will be an excess supply of money. As that money is spent on the various goods, the price level will rise. This will raise nominal expenditure and nominal income, but deflated with the higher price level, real income and and real output remain the same.
A nominal GDP target would have the same effect as a fixed nominal quantity of money (or a gold standard with a fixed stock of gold.) To the degree the sole proprietors understood the nature of the regime, they would not expect lower nominal demands for the products, and would respond to the decrease in supplies by charging higher prices. Oddly enough, this is what they would do if they were truly ignorant of the nature of the problem, and simply took the decrease in productivity to be peculiar to their own market.
A price level target, on the other hand, would allow the price level to remain stable. With a fiat currency serving as medium of account (and medium of exchange,) its quantity would need to be reduced in proportion to the decrease in the supplies of the other goods. But then, nominal income would fall with the reduced real output and real income. Interestingly, if the demand for credit is positively related to real income and real output, and interest rates are pegged by the central bank, then it might "automatically" reduce the quantity of money in line with the reduction in real income and output.
This scenario has approximately no connection to the real world. While uniform productivity shocks are possible, self-employed sole proprietors? Unfortunately, it does have a more than passing resemblance to the models used by mainstream macroeconomists.