I'm not a statistician, just a biologist. But I have seen some pretty low P-values indicating two distribution have a differing mean while the plot right on top

I'm not a statistician, just a biologist. But I have seen some pretty low P-values indicating two distribution have a differing mean while the plot right on top of each other. This is when there are a lot of measurements (in my case there were over 100.000). I prefer to make ROC curves or simple just to look at the plotted distributions. ROC curves give a nice idea about the mixed-ness of positive and negative measurements.