If you have your own in-house servers or have a cloud server with the freedom to configure any PaaS that you want, then Dokku is for you. So far, I have never run into a scenario where Dokku was not able to fit my needs, after deploying many different types of applications with varying frameworks, languages, and connected services. If you already have a PaaS available, however, Dokku may not be for you.
In our organisation we are the only team that uses Platform.sh to host any site. This was a cost effective way for us as we were using Acquia Cloud earlier for these websites. We mostly use Platform.sh for those sites which are always in development as it is simpler and faster to handle these operations in Platform.sh. Then we do a lift and shift to Acquia as we move more towards the go live and post production maintenance side.
Dokku might overreach on its assumptions about how you want to host your app, using its own VHOSTS plugin by default. This may be a pro or a con depending on what you want.
Proxy port configuration can be somewhat difficult, with Dokku resetting any pre-deployment configuration to "smart" defaults on the first deployment.
Platform.sh is not for beginners in my opinion. It has a good amount of learning curve in my opinion.
As this is a PaaS, teams habituated with cloud infrastructure may miss the server side support from their cloud teams. I believe you will have to work on server bugs more on your own.
During normal maintenance periods, integrations may fail if you are working on your sites in that time, in my experience.
Dokku is incredibly well documented and also takes advantage of the documentation and community of Heroku, being essentially the same thing, but in the case that you encounter an actual bug or issue, it can take time for a fix to make it into a new version. Since you manage Dokku yourself, there is no support team to call for help.
Dokku is essentially the same thing as Heroku, except maintained by you on the platform of your choice. If you have any experience using Heroku, then you will feel right at home using Dokku. Dokku is an entirely free to use PaaS, requiring only that you have a platform to deploy it on, making it far more versatile than Heroku in my opinion.
In our team we use Platform.sh mostly while sites are in developmental phase. Then we do a lift and shift to either Acquia or AWS depending on the type of sites we have. Platform.sh is really cost effective and more fluid in terms of Continuous Development hence the usage. After said development is done, we generally lift and shift to Acquia for more content heavy sites and to AWS for more transaction oriented sites.
