It's been a decade since I did my long trek through Roman history, but as I recall there actually is quite a bit of debate about whether he said that and if he did, whether he said it at the time (or closer to/on his deathbed).
It's depressingly amusing to me. Odd choice of words, but it's the only way I can put it. He didn't give two ****s about Christianity (most of that was written in later because....well, remember who writes the histories? The victors) or even what version was the truth. He wanted to put the other-faith vs. Christianity thing to sleep and then he wanted to put the inter-sect fighting to sleep, so as to save the Empire. He was well aware that some parts of the system had become unsustainable, ie, the need to constantly expand the Empire to obtain more troops to defend on those enemies on each new set of borders, but he also wanted to keep it going. So cut out internal conflicts, cut out alternate power structures (hence a few hundred years earlier, the execution of a certain Jew with a following by nailing him to a cross).
As an example, the council of Nicea. He gave less than a two hundredth of a **** about whether Arias or Athanasius got the trinity theory right. He just wanted the two factions to stop the fuss that could lead to a civil war. So he let the people argue, let Arias take his abuse, and sided with Athanasius. He just wanted it settled. That's it.
Assuming he actually did claim this - again, that's up for debate - it would be to ensure that the empire did not fall back into internal squabbles between the alternate power structure of religion. By doing a thing like that, he would help cement Christianity as *the* religion, and thus at least partially incorporate the clergy's alternate power structure into the empirical structure. He did keep the Western Empire alive another 250ish years and the Eastern? Well, the Eastern turned into the "Byzantine Empire" and lasted until......I want to say 1493. Bloody Ottomans.
One battle with so many consequences, or is it one statement with so many consequences? Either way, the amazing point is that the effect went so far beyond what Constantine was thinking at the time he made the statement if he made it. If someone else made it, it had the exact effect intended and was the most successful bit of propaganda in the history of mankind.