Even though it is widely used, the Sharpe Ratio has a flaw: it includes not only the downside volatility (the part we really care about), but also the upside volatility (the part we would like to have!). The Sortino Ratio corrects for this by modifying the Sharpe Ratio. It uses the downside deviation rather than standard deviation as the measure of risk — i.e., only those returns falling below a user- specified target (“Desired Target Return”) are considered risky. Movements cause by upside volatility -- prices moving higher -- are ignored.
In other words, the Sortino Ratio only uses downside moves in its volatility measure. The Sharpe Ratio includes deviations both above and below the average returns.
The Sortino Ratio is generally a better measure of risk-adjusted returns than the Sharpe Ratio and like the Sharpe Ratio, the higher its value compared with its benchmark, the better the risk-adjusted returns are.
Click here for a good paper of the Sharpe vs Sortino Ratios.