Which data is "more normal"? I have two sets of data, and I want to test which is "more normal" (specifically residuals from two different models fitted to hourly and daily data - the daily data is the hourly data aggregated).
One appears "more normal" when plotted as a Q-Q plot. I've also performed a Anderson–Darling test and in both cases the p-value is < 0.05 but in one case > 0.01, the test statistic itself is lower for the "more normal" data.
My question is, is it valid to say that on the basis of a lower test statistic between two tests that one of the data is "more normal"? Particularly if neither meet some level of significance?
 A: Let us begin with the assumption that you have data collected across time that is drawn from a normal distribution.  If it is, then the frequency is irrelevant even if one level of frequency looks nicer than another.  That is due to Donsker's Theorem.
As to 

My question is, is it valid to say that on the basis of a lower test statistic between two tests that one of the data is "more normal"? 

The answer is no, at least as you have constructed it.  Your null hypothesis is that $x$ is drawn from a normal distribution in both cases.  It is rejected.  You cannot, at least in this manner, make statements about the differences in the samples.  You did not perform a difference test such as $\mu_1-\mu_2$.  Hypothesis tests are with regard to population parameters and not samples.
You have two choices on how to consider this, subject to the assumptions of the Anderson-Darling test and any instrumentation issues that may have existed in gathering the sample.  You can either use the p-values as evidence against the null and reject that it is normal; or you can assume that the sample is an extreme case because the p-value only states that if the null is true, then the sample was unlikely. If the latter may hold, then you should perform another investigation.
By themselves, p-values are not informative as to whether your sample was bad but your hypothesis good and the case where the sample was good but your hypothesis bad.
The better question, regarding your residuals not being normal, is "so what?"  Why would they be something else?  What might be going on in your model?
