It's just a choice you have to make. Google analytics tracks pages by both page title and url. Depending on how you are viewing the report, your new pages with the same page titles will still aggregate together (so the data will combine), whereas when viewing by page url (if the urls have been moved) will show up with new entries (and the data will start over). When viewing the content overlay reports however you will get some odd data because your content has changed.
I personally would just use the same UA number. This will also allow you to easily compare the performance of the new site vs. the old by comparing the data range moving forward to the date range before the site was redesigned. I have done this with a site and it worked well for tracking performance changes.
You should also consider the SEO impacts of making drastic changes to your site. That is a whole other issue altogether.