The problem of having more than one URL pointing to the same file is not primarily a human usability problem (since humans can easily figure out they're looking at the same page). It is a search engine problem. Website Designer have written about this problem at length elsewhere, such as in the article How to Create a Search Engine Friendly Website. If you have not read that article, please read it now before continuing further. I shall assume you understand the issues of content duplication in the rest of this article.

In view of the problems discussed in that tutorial, if there are two or more ways of referring to a particular web page on your site, you should always decide on one URL and consistently use that on your site. For example, decide whether you want to refer to a page as www.example.com/about/ or www.example.com/about/index.html. Once you've made that decision, make sure that all web pages on your site link to the page using the form of URL that you've settled on. Your site map, whether a normal site map or the search engine specific site map using the sitemaps protocol, should also refer to that page with the same URL.

If your site is in the same boat, and you have a change of heart about what constitutes a prettier URL, you too may have to resign yourself to your current form for practical reasons, as I did.

Don't spend too much time mulling over whether to use the directory name or the index file form of URL. In practice, it probably does not matter which you use. Just decide on one form and stick to it. The important thing is to be consistent. If you have referred to a file as example.com/about/ in the past, continue to refer to it as such and don't link to it in other places as example.com/about/index.html. This applies to both your web pages as well as to your site map.