Aurelius and Constantine

I've previously discussed my distaste for sloppy counterfactuals, but here's a great counterfactual from Mill that is actually worth thinking about:

It is a bitter thought, how different a thing the Christianity of the world might have been, if the Christian faith had been adopted as the religion of the empire under the auspices of Marcus Aurelius instead of those of Constantine.

As a Sigma Chi I probably ought not speak badly of Constantine, but this really does raise some interesting historical questions of which I must confess the greatest ignorance. What was the effect of Constantine being the great patron of Christianity? Is the militancy and intolerance of the Crusades/Inquisition/etc at all traceable to this accident of history? Would Aurelius really have done better?