Depends on what you mean by better.
Take away the prize money and you take away most of the elite runners. You'll end up with a field of mainly 2:20+ runners. Some very good Americans and perhaps one elite if you're lucky. The prestige will always bring a few fast people, but most will go elsewhere looking for money.
Regardless, the Boston Marathon will always be a very big deal around Boston. It's got too much history. And fortunately its prestige was not built on prize money. Go to Chicago, London, or Berlin and you're running a different course every other year. At Boston, you run down the same streets that Clarence Demar ran. I doubt that means much to Kenyans, but it means a hell of a lot to the 20,000 or so runners who pay the bill.
The people will always come out in the thousands to cheer for the runners. You'll always have some local sponsor willing to put up money for just being associated with it. Charity runners will still show up by the thousands to raise millions for charities. Is that "better"? Probably not. But I don't see that it's any worse for Bostonians either. Just different. It's not a such bad fate to be (as someone else put it) like the Marine Core Marathon.
In the end, what did prize money do for Boston? Well, it turned it into the Kenyan national marathon championships, that's what it did. Or the Kenyan Olympic Marathon Trials. It's a privilege to see such incredible runners go by each year but I remember watching even in those "terrible" years of 84 and 85. It hasn't made Boston "better." Merely faster.
But the point is moot. You have to be realistic. Prize money is here to stay at Boston. We're always going to get fast runners. Now that we offer less money than Chicago, London, and Berlin we won't be getting the Khannouchis and Tergats of the world. Just some Koreans and the Kenyan "B" team. I can live with that. Give me a good duel between some fast guys and I don't care if they're running 2:20s, really. I just want to see a good race. Or run it.