Cramming the same old code, CMS, application, etc into the cloud (any cloud) doesn't make the most of the capabilities of cloud computing in all it's various forms. I expect to be discussion this subject more in the near future. But, start by giving two examples and labeling them cloud native application design pattern and anti-pattern.
A Cloud Native Application Design Anti-Pattern
I'll pick on Drupal a bit (but with love). If one installs Drupal at a cloud IaaS or PaaS provider then that does not make Drupal a cloud native application. To me, this seems obvious but I am not so sure it is obvious in general. The Drupal CMS is not a Cloud Native Application. Putting Drupal, Wordpress, CMS XYZ of your choice on cloud computing IaaS or even PaaS provider of your choice essentially means you end up with an virtualized n-tier application running in the cloud with many of the same limitations of a hardware based deployment and only some of the benefits of being a cloud native application running on a cloud computer. Yes, of course, and admirably (see billions of pageviews per month) drupal can run IN the cloud. But, that does not make it OF the cloud. But, I will say that based on personal experience even considering all this situation it's still likely the right choice in a great many cases to run it in the cloud.
A Cloud Native Application Design Pattern
If you want to see what CMS can look like as a cloud native application then check out the Lily CMS project. I personally might not choose this specific architecture and systems design to achieve the same goals. However, there is more than one way to build a CNA. They have done some great work there and are clearly on the right track! It's excellent work and I have respect for what the Outerthought team has created with their platform. It's actually potentially quite a lot more than just a CMS as well. In any event, I think that with the exception of the default HBase high availability limitations (which will be addressed soon by HBase project I suspect) this can be considered a cloud native application. Coupled with the appropriate monitoring, automation, and even cloud environment awareness it would be a very powerful cloud native application.
All of this summarizes to me as one very simple fact. There is a tremendous opportunity ahead! Exciting times.