Money and fame are often touted as two sides of a coin, and while they are independent entities, either one can be used to get the other. If you look around society, you'll find that there are actually different people who stand at different ends of the fame spectrum, despite being at similar financial status.
There's a strong similarity between fame and wealth, despite being mutually exclusive entities. Their mutual exclusivity actually rests on the application of which one the individual has. So a rich man may not be famous, and a famous man may not be rich, however, either could be both through the application of the one you have.
There a lot of rich men on earth, I think at this moment, there are about 200 Billionaires in dollars, with a cumulative net worth bigger than a lot of countries. Two men who stand at the top of this list of rich boys are Bill Gates and Warren Buffet. These two business moguls built their empires and have so much many, they don't have to work a single day of their lives.
To elaborate on the point of fame vs wealth, you can check the relative popularity of these two individuals who have a similar amount of money. Putting it simply, Bill is way more popular than Warren, and this is by a stretch.
I've also found that the idea or possession of fame or wealth also depends entirely on the individual in question. Old school people like Warren, who made their money from Hedge funds and silent investment will most likely not hog the spotlight like Bill who got his wealth through actively marketing his products and riding the wave of the initial fame his product brought by constantly reinventing and improving the quality.
So money doesn't translate to fame, and vice versa. So with that in mind, your personality and every other variable considered, which one do you want?