Shapiro Wilk's tests normality by comparing a distribution to the standard distribution and it works well with values that are unique. In other words, the values should be more continuous and non-repeatable. On the other hand, KS is a non-parametric measure that actually tests goodness-of-fit and works well when you are comparing two samples rather than a sample with standard distribution. My advice would be to go for Shapiro Wilk's first and have KS as a backup. Also, I would not only rely on values but also would want to look at histograms and Q-Q plots for knowing whether or not my data are normally distributed.

Shapiro Wilk's tests normality by comparing a distribution to the standard distribution and it works well with values that are unique. In other words, the values should be more continuous and non-repeatable. On the other hand, KS is a non-parametric measure that actually tests goodness-of-fit and works well when you are comparing two samples rather than a sample with standard distribution. My advice would be to go for Shapiro Wilk's first and have KS as a backup. Also, I would not only rely on values but also would want to look at histograms and Q-Q plots for knowing whether or not my data are normally distributed.

Both Test are for assessing the normality of the data, simply KS is for the larger sample size and SW used for data with the smaller size

I would recommend against using any test to test for normality.  They are sensitive to sample size, so they probably are not really answering the question you think they are.   Instead use a histogram or a quantile-quantile plot.  Your eyes will be a more reliable judge.

See: http://blog.fellstat.com/?p=61 .

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