If you are completely changing the structure, theme of your website, my advice is:
Do not make all the changes together.
Googlebot and users do not like websites that are completely changed. For example you might have a blog and 100 direct readers. Your readers know the structure of your website, they know that on the right top there are the popular posts, at the home page there are some interesting widgets etc, they can easily navigate through your website.
If you completely change the website, some of them will leave. Also Googlebot and specially if you are using Adsense, will start to re-validate your website, and you possibly see that your rankings and earnings are going down, and you will need weeks or months to reach your old earnings.
To sum up:
Do not have 2 versions of the website (duplicated links) for any reason (as Martijn also said) this will destroy your SEO, and make the changes one at a time.
Stay with the change for some days and continue with the next change, so Googlebot and your readers are get used to these changes.