The two are part of two different standards. They shall never meet. For the HTML Description Meta-Tag, that would describe the entire page. For the Itemprop Description, that would apply to only the content segment you are marking up.
There may be cases where it is appropriate that they are the same such as a product page within an e-commerce site. It is all up to you and what you think is right for your users.
Always create content for your users and not machines.
There is no effect if these two elements are identical or not. While the HTML Description Meta-Tag is used for weighting a page within a search engine and can potentially be used as a search engine results page (SERP), that is the extent of the HTML element. The Itemprop Description will not be taken into account the same way. The intent of mark-up is to mark-up segments of your content as data so that it can be properly read and ultimately parsed into a database. Google, for example, will trust what it is seeing more when the content is marked-up. This has limitations of course. For now, it does help with the semantic understanding of content and what to do with it in regard to better search results.
For these reasons, both should be the best you can devise for whatever purpose they serve.