The answer is of course either but rarely both at the same time. With e-marketing the potential to reach your niche is more possible than ever. Google "The Long Tail" for more on that and Seth Godin in his brilliant blog and books also has a lot to say on this one too.
Even with a broad product base you should still be segmenting your customer market and creating a unique mix for different segments.
Personally I love to work within a niche. It is great to connect so much more personally with your customers, Google adwords are cheaper, there is less
SEO competition for organic listings and its possible to become a major player in your niche.
For the marketing theory on this debate you want to look up Michael Porter's Generic Strategies. I often find it helps to read around the academic thought on an issue before applying it to my business situation.