How to decided which test of normality to use
Mathematical detail of the two different tests can be found in two papers:

[1]. http://sci2s.ugr.es/keel/pdf/algorithm/articulo/shapiro1965.pdf

[2]. http://www.jstor.org/stable/2334522?seq=1#page_scan_tab_contents

To summarize, both methods are based on hypothesis testing. But they are using different test statistics. 

Shapiro-Wilk test has many good analytical properties and was designed to apply to data with sample size less than $50$. However, when the sample size becomes greater, Shapiro-Walk test might be unreliable. As I quote from the second paper:


  Shapiro and Wilk did not extend their test beyond samples of size 50. A number of reasons indicate that it is best not to make such an extension. 


Essentially, that is why people invented the second normality test. As I quote from the second paper:


  We present a new test of normality applicable for samples of size 50 or larger which possesses the desirable omnibus property