Focusing on a niche market rather than the broader market? A good idea?

We are a start up just building our website and are considering whether to focus on a niche market or to sell to the broader market.

Does anybody have any experience of being in a similar dilemma and what was the outcome of your decision?

Did you decide to target a specific niche?

And if so, are you happy you did so?

All advice and suggestions will be well received.