I guess this all depends on how we define success. I started on this thought process as I was trying to optimize this website. Doing some keyword research it appears that searches for "happy" are many times more popular than searches for "success". So it seems that according to Google, people are more interested in happiness than they are in success, of course "money" was also up there with happy.
Some friends and I were discussing this and it appears that people generally think about material things, like money, cars, and houses when they think about success. This is understandable.
When thinking about happiness, they don't necessarily equate that to physical abundance. Take monks or other devout individuals that specifically deny worldly pleasures in order to achieve enlightenment, which I assume is a form of happiness.
According to The Happiness Project "...money can’t buy happiness, but it sure can buy lots of things that contribute mightily to happiness." USAToday takes the other view "Money can't buy happiness, but happiness may buy money".
I hope to maintain both states of happiness and success. The people that I know well personally that are financially successful are also some of the happiest people I know. I am working to follow their lead. If I have to choose though, I would choose greater success for less happiness.
How about you, if you had to trade off happiness and success which do you value more?