If you have two pages with the exact same title but with different content, what does google do? Choose which is highest quality and then throw the other into supplemental index? Or rank both but one much higher?
In most cases, Google will display the home page, the page that contains more keywords on a particular topic, which has more links. In any case, it looks a little different. If you have the opportunity to differentiate the titles of your web pages then do it and do not think about it what if...
Google ranks both the pages, and will rank the page that it finds higher in quality and more matching their guidelines. There are several websites which have 20 odd articles on the same topic and with the same titles and all of them get indexed and rank well on the SERPs too. Sites like Buzzle, EzineArticles, etc. have dozens of articles with the same title both indexed and ranked well.