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Just to echo other responses, I wouldn't do anything to take away from one of the pages, but just continue any branding and link building efforts to just one of the pages. Adding a link from the secondary page to the primary page will help. The notion that hurting one page will help the other doesn't really jive--just focus on building reputation for the page that matters.

The reason I would like to make the change, is to make the urls easier for visitors to remember, also, to make the urls look more professional. I personally feel that example.com/blah.html just looks kind of sloppy. Thanks for your answers.

Sounds like you need to sort out a canonical URL issue. In your .htaccess file, redirect /index.html to www.example.com. It's easy to 301 it but you may also have non-www and www issues. If you're not sure what I'm talking about, check out that link above and it might make it all clear. This should stop the XML sitemap generating the two pages.