New money seem a bit insecure in their position. They're usually described as feeling the need to prove their wealth some way. Old money are, in a way, slightly oblivious to the extent of their wealth and can't tell when they're flaunting it or not. Like, I live really close to an "old money" family and they're the kind of people that have two mansions right next to each other, but they go out driving in their Lamborghini wearing a raggedy t-shirt and a pair of flip-flops. They don't care how people see them because they're just that rich and could probably buy your extended family.
I guess there's also that aspect of a person working hard to live a lavish life, becoming "new money", and finally getting to live the life they've always wanted to live. Why would they hold back when it's something they've been working towards for so long? The stuff they buy is probably more for their own satisfaction rather than to flaunt superiority.