In a very simple paper "Sharpe & Sortino - Does it Matter", Linus Nilsson present his findings on comparing the Sharpe and Sortino ratios. The correlation between the two risk measurement approaches is very high regardless of the strategy set used. You may think there is added value with using more complex risk measurements, but you will still get the same answer. This does not mean that you should throw-out other measures, rather the conclusion is that you will not get any more information from these alternatives. This similar risk comparison is even the case when there is positive skew with a strategy. The sample must be large to make a distinction.
Nevertheless, this works does not change our earlier view:
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