Constantine was a politician. He was credited with making Christianity the official religion of the empire because of his famous vision of the cross and statement that under this symbol he would rule. I suspect that his real purpose was two fold. He was trying to appeal to a growing movement and cement his political power with their support. The other reason may have been to avoid having to deal with the intrigues created by the complex Pagan religious tangle of competing temples and priests vying for power. Monotheism is so much neater for the leader of an empire, especially if the monotheistic religion also hints at the divine right of kings.

This doesn't mean that Constantine created Christianity. But he certainly did use it for his own purposes. It's also likely that he influenced it in a direction that was beneficial to himself.

To get back to the original question of how things might have been different if he had co-opted Hinduism instead, I don't think he ever would have. Hinduism was too much like the existing religion of Pagan Rome to have been attractive to him. He still would have had to deal with multiple temple all vying for supremacy. There was no benefit to him.

One of the powers of Christianity from a rulers perspective is that not only could it be used to support the divine right of kings (and also Emperors) but there was no legitimate alternative path. In a Pagan religion, if you don't like a priest's proclamations, you can find another temple with a different God or Goddess that is more to your liking and there's no risk to your soul. With Christianity, if you don't follow the rules, you're going to Hell. What dictator (that's what kings and emperors really are) wouldn't love a religion like that?