I would like to run different websites with differing design and offer the same products using different prices.
When you say different website, do you mean different servers, different domains?
If the only commonality is the the products, it might just be easiest to export/import them between the two, and change the prices according.... either directly via phpmyadmin, or else there is a joomla module called CSVi that can do import/exports.
Hope this helps.