# Can I use K-S statistic to determine best fit even when the null hypothesis is rejected?

I'm comparing data from two different models, I also have the real data. I want to demonstrate that one model fits the real data distribution better than the other model. Unfortunately none of the models are proved to fit the same distribution of the real data, since hey are having very small p-values when performing KS test. Nonetheless, I think that since KS statistic is a measure of the distance between two EDF, the model with the lower KS statistic is the one who fits better to the real data distribution. Even though it's not reaching the significance level, I think it can be said it's still better than the other model. Is OK to do that?

If you can give an idea about what my data fails in not rejecting the null hypothesis, it will be good too. Bellow are some q-q plots of my data, I think they are showing a pretty good fit to the observed data, so I don't really know why they don't fit to real data according to KS p-value .

Thank you, I hope you can help me.