Expected goals predicts the correct home team result 66% of the time and away results 58% of the time. This is slightly better than shots on target on the away results and slightly worse on the home results.
For the astute among you, it can be seen that shots on target and expected goals provide similar results in predicting the outcome of a match.

Standard Deviation of Results

This is correct in a sense, but the above calculations are based on the shots and expected goals that occurred within the individual match i.e. predicting the outcome after the number of shots and expected goals are known. The biggest difference is that teams have a lot higher standard deviation in shots on target versus what they do in expected goals (3.6 vs 1.2). For anyone unfamiliar with standard deviation, it just means that the lower it is the smaller the spread of outcomes from the average. For example, a team over 5 games may have shots on target of 2,6,7,3,2. This shows a large variability in outcomes away from the average of 4. Conversely, expected goals will often look like 1.5, 2.8, 2.5, 2.2, 1.4 which shows a lot more consistency and translates to the real life amount of goals that should have been scored.
Due to the lower variability in outcomes, expected goals is a far superior tool for predicting the expected goals a team will score and concede in any future match.