Processors with more cores use more advanced technology, that's why they're more expensive. If you add up the processing power, then in theory they're faster, but in practice it depends on you using software that works across multiple cores.
More power won't mean much unless you're running computationally expensive operations. It's hard to judge if that's so without knowing what you're doing; in general, if you're building a webapp then it might be useful, but if your just hosting websites then less so.
CMS platforms often consume a bit of power when they query their database and also some when they render the pages. However, it's often better to look for other ways of speeding up a site, like using caching and CDNs; For example, I'm using the CloudFlair service at the moment and a large amount of requests to my site never actually get near my server.
Using more cores for web hosting usually makes your server able to handle more requests simultaneously; meaning that more people can access your site at the same time without being slowed down. However, as I just mentioned, there are ways of avoiding people hitting your server at all, and other ways to make their visits consume less CPU cycles anyway.
I know you're not looking for a recommendation, but I'll give one anyway! I think you're best off testing your site out on a cloud platform like AWS or Rackspace first; you can try out different sizes and configurations of server without any commitment beyond paying per hour of usage. Once you've decided what's going to work and what your future expansion plans are, you can then decide if it's going to be cheaper to commit to a dedicated server or stay with the flexibility of the cloud.