It's better to be happy than not happy. Rich/not is something different. I know many people in varying degrees along that scale and their happiness does not seem to be correlated to their wealth. Many in the lower end of the scale believe their happiness is tied to it, though.
When you say that happiness does not seem to be correlated to wealth do you mean that having a larger salary does not seem to be correlated to wealth or that having a more savings/less debt (to some extent this is two scales, to some extent it is one scale) does not seem to be correlated to wealth.
I find it hard to think of someone whose annual income is in the 200k+ range but who is in massive debt as rich or wealthy. Similarly, someone whose annual income is below 50k but who has no debt, owns their own home free and clear and has massive savings could easily be thought of as wealthy. Of course, "massive" when talking about money is relative to income and debt/savings are likely to be orthogonal to happiness to a large extent. With regards to money and happiness, I think the Micawber principle states it best: "Annual income twenty pounds, annual expenditure nineteen pounds nineteen and six, result happiness. Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery."
