I imagine there's a real difference between staying on the Mont, compared to staying near the Mont. Yes, you'd give up the view but could always make the trek to get a photo at the appropriate hour, then go back. I was there some years ago and we had no plan regarding where we'd stay. It was off-season so we weren't worried. We found a very modest, friendly hotel on the main street as it begins it's climb, with a view of the cobblestones below and it was perfect. But then, under the circumstances, I think anyplace would have been perfect, I was so enthralled with the place.
It simply depends on your priorities, of course. There were a couple of posh accommodations and the rest were modest. I suspect, if you make an early decision, you'll be able to find an affordable room on the Mont. I like to be inside some experiences, observe others from a distance. In this case, I'd again choose within.