Can you compare p-values of Kolmogorov Smirnov tests of normality of two variables to say which is more normal? I have applied the one sample Kolmogorov Smirnov test of normality to two variables and one has a larger p value but both are greater than .05.
e.g., 


*

*$x_1$ (p-value) = 0.09 

*$x_2$ (p-value) = 0.06 


Does this mean that $x_1$ is better or more normal than $x_2$?
 A: In general, the lower the p-value, the less belief you attach to your null hypothesis (in fact, the p-value is the chance that, if the null hypothesis were true, a test statistic so extreme (or more) as the one obtained from your sample would be obtained).
As such, it is reasonable to say that the lower the p-value, the more confident you are that there may be an alternative out there that is more probable to give this extreme statistic. As we are typically aiming to dis"prove" the null hypothesis (e.g. show that a coefficient in a regression is not zero), typically we say that lower p-values imply better results.
With the K-S test, it's a bit different: in fact, here, we typically hope that the null hypothesis is true. Therein lies the problem: at "best" we can say there is overwhelming evidence that the null hypothesis is not true (when the p-value is really low), or that the test we used did not provide evidence against the null hypothesis (e.g. if you find a p-value of 0.5). Unfortunately, there is nothing to say that there isn't an alternative out there (for K-S it could be e.g. the T-distribution instead of normal) that would give even better results!
In this manner, it is not a good idea to call the higher p-value "a better result". At most you could say that there is "less evidence against" its null hypothesis.
If there is some sound reason for applying the hard threshold of 5% (which in truth generally is rather arbitrary), it doesn't matter anyway, like you indicate.
A: Read this article:

Murdock, D, Tsai, Y, and Adcock, J (2008) _P-Values are Random
 Variables_. The American Statistician. (62) 242-245.


It talks about the fact that if the null hypothesis is true then the p-value is a uniform random variable.  This means that you are just as likely to see a p-value of 0.09, 0.06, 0.01, or 0.99.  (when the null is false in a way that the test is designed to detect then the p-value is a random variable with values closer to 0 being more common).  
Here is an added example (in R):
> out1 <- replicate(1000, ks.test(rt(100, 10), pnorm)$p.value )
> out2 <- replicate(1000, ks.test(rt(100, 50), pnorm)$p.value )
> 
> mean(out1 < out2)
[1] 0.522

This simulated data from a t distribution with 10 df and a t distribution with 50 degrees of freedom and does the ks-test on each simulated dataset and gets the p-value.  Then it looks at each pair and sees how often the p-value for 10df is smaller than the p-value for 50df (the 50df should be "more normal" than the 10 df).  But the simulations only get this right 52.2% of the time, only slightly better than flipping a coin.  I would not want to base any important decisions on something like this. 
Now if you are comparing something that is very non-normal to something close to normal, then the p-values will probably show this, but then a simple histogram or qqplot would also make this obvious. 
A: The smaller p value represents stronger evidence against the null hypothesis, but it may not be that the first distribution is "better or more normal" than the second. Instead, it may be less easily distinguished from a normal distribution.
Note that the amount of evidence against the null hypothesis in a p value of 0.06 or 0.09 is quite small. However, if your samples are small then the power of the K-S test to provide evidence is also small.
