It depends.
Someone who works 80 hours a week in a high stress job making a 1 million dollar salary is going to be a lot less happy than someone working 20 hours a week making 100,000 a year. With that being said, given equal conditions other than money, I would think that people that have more money would be slightly more generally happier than those with less money.
There is a cutoff to this though, which I would put around 100K a year. After that I think things would start to level off. A large study said that things start to level off around 75,000 or so, but I think it would be a little higher than that.
How Much Money Do You Really Need To Be Happy? - Forbes
Happiness truly is a "state of mind" rather than what possessions you have, or how much money you have. What we call happiness, in my opinion, is simply how much and how often you release "feel good" brain chemicals such as serotonin, oxytocin, norepinephrine, dopamine, and many others. Granted you can sustain long releases of these chemicals through the use of money by buying experiences, vacations, etc., and even buying material possessions releases these brain chemicals.
However, the problem is that the "chemical release" during these actions using money diminishes very rapidly, so it is not sustainable. Thus the reason why you see people that are very rich, that are absolutely miserable even though they are taking vacations every other week, buying sports cars, and doing many other things on a regular basis that make us "happy".
The best scenario, in my opinion, is to create a happy state of mind without the need to constantly maintain through monetary means. Once you are able to do this, then you can proceed to purchase the material possession and buy the unique experiences, and you will enjoy them even more because your are already "happy" to begin with, so your essentially adding on to a firm foundation of happiness rather then building a rickety house of happiness using money. But you also have to be careful not to get caught up in all of the material things, and begin to rely on them.
Understanding LOVE
If you read the first section it presents an interesting view on happiness. Monks literally live in a state of constant happiness due to their attitude of love towards everyone, their detachment to the material world, and most importantly in my opinion, their meditational practices. So all you really need to be "happy" in my opinion is to have your basic needs of water, food, and shelter met, and also be well versed in meditational practices. The brain scans of monks, who literally have no money, show this to be true.