I think I'd be a hell of a lot more happy in life if I had more money (for instance, being able to travel someplace far without worrying about money would be great to help me refresh whenever I'm stressed), but it's absolutely not the be-all and end-all of happiness. It really depends on what you do with it, and whether you let your wealth affect your life. I personally wouldn't go around telling everyone in my life I'm loaded, not even my family, because it complicates things a lot.
As for the question of the OP re: happiness vs wealth, I do believe you can have both. If I couldn't I'd rather be rich and save up a shitload of money for like 5 years as an investment, then shift towards a career I'm happy with. My peers have actually done this, but I haven't really felt the need to do the same.