Product Duplication

It's either you reword your categories for the other site or think of other categories altogether.

The products listed in categories are going to have little to no SEO benefit to them (and certainly no "duplicate content penalty", as if there is really such a thing). It is the words on the category page that separate one site from another.

Far too many people just slap up a category page, put products on the page and think that they are done. I assure you, that category page has little chance of ranking for anything because there are no actual words on the page other than product names (it's just a page of links, really). There is no value added to the internet.

Put words on those category pages that introduce the category, highlight the most popular products, help people distinguish the products from one another. We like to put a category-specific FAQs section at the bottom of category pages. All of those words are what keep one website's category page from being the same as another website's category page.