Two of my aunts are absolutely loaded but they seem to deal with money quite differently.
Aunt 1, very high income (as does her DH), owns several properties etc... and has 3 children (who are the same ages as me and my DBs) she has no problem spending lots of money on herself and her DH and is always driving the latest car and buying a bunch of designer clothes and traveling the world. Her kids on the other hand seem to only get what they need. They do get a lot of what they want for christmas but it's nothing too fancy or expensive (basic video games and/or toys), my oldest cousin though did get a car when he got his driving license but it was a very old second-hand car that was only bought so he could get to his classes/work, so nothing fancy whatsoever. They also don't get to join in on the trips abroad as more often than not my aunt and uncle go abroad while the kids stay home, so I think they are aware their parents have money but I don't think, they actually think, they personally, are rich.
Aunt 2, husband has a business that's doing very well so they now own many properties and businesses and recently just had a baby. I think they are spending a bit more now that they've had a baby (on him) but before that it wasn't uncommon to see my aunt driving a car on the verge of breaking down even though she owns a Maserati that's the price of my house collecting dust in her garage. They do a few trips but it's mostly trip to Spain or Italy and very rarely go farther abroad. At chrismas they seem to be gifting each other very basic things and you would struggle to know how rich they are unless you knew them personally.
That being said, I once Au Paired for children of a very rich family and there it was all about flashing money, kids getting very expensive stuff: piano, designer clothes, real-life size doll house in bedroom and the like. They were quite generous with money and gifts though, with me at least, as both the mother and the grandma handed me over a couple hundreds of bucks each as well as expensive jewlery as if they were just handing me over a few coins and a bit of tat. 
I was shocked as the most I have received from my rich relatives must have been 10 bucks at christmas (from Aunt 2).
So overall I would say that most rich people don't tend to do gift as much as poorer people (I come from a very poor background but I still think my brothers and I were overall more spoiled at Chrismas by my parents than my cousins by Aunt 1) which I think is due to the fact that they can litterally afford everything they want all-year round so there is absolutely nothing to excitedly wait for on christmas day or birthdays.