Actually, people don't really fight over money. They fight over the prioritization of money and spending. Between couples, if the guy has more or the girl has more, there's not really much to fight. Usually each party doesn't try to grab the other's money. 

Money is simple. You either have it, or don't have it. 
The disagreements come about during the prioritization of money.
Or in simple terms, when there is a limited amount of money, how to allocate it. 

For example, the wife might want to save for the future, and for their kids in future. 
Whereas the guy wants to buy a bigger car.

Or the wife might want to send the child for classes and enrichment.
But the dad might think it is pointless cos, last time I didn't go, why does the kid need to go now?

Or the wife might think, why did you buy Mau Shan Wang