We're not sure if Canonical will do their best to increase privacy levels for Ubuntu but it seems that they're already do so and Android is one these OSes they want to teach a lesson of.
For some reason, switching from Mac OSX or Windows to Ubuntu is not recommended probably due to some privacy issues but there are some workarounds.
You can uninstall the unity-lens-shopping package from the terminal or something and disable Include online search results in the Privacy app. Not enough? Then you can switch to other desktop environments such as KDE, GNOME or Cinnamon. Just install one of them, log off and switch the desktop environment from the login screen and log back in.
Next is the installation of Ubuntu. During the setup screen, you can encrypt the new Ubuntu installation for security purposes. That is, before the installation process begins. Then, you're given the security key screen to enter your security password. This is probably the disk encryption and if you lose or forget this security key you have made, all data will be inaccesible and lost.
Another thing from EFF to Ubuntu users is that you may need HTTPS Everywhere extension for Firefox and Chrome.
Well, that is more of the summarized news divided into two parts from EFF website. We hope that Canonical can show Google on who's boss in privacy.