Which would you recommend to your boss, Amazon AWS or OpenShift?

It really depends on the use case. I have used both for different projects. Including deploying Openshift cluster on AWS but to keep this response somewhat simplified, keep in mind Openshift is really a CaaS (Container as a Service) offering and layered over Kubernetes. Whereas AWS EKS and ECS are managed services (so yes, PaaS). If you need to DIY (do it yourself) or have functionality closer to native Kubernetes and want to manage your own cluster (or required to do so for various compliance reasons), then Openshift distributions (whether OCP - this costs more due to Red Hat support; or OKD - completely free and open source) from Red Hat are very good CaaS solutions. If your project compliance and costs allows cloud service providers (like Amazon in this case, or even Azure in other cases) to host your containers using the CSP managed services, then AWS ECS or EKS are fine solutions too in those cases.

I would second Shivali mentioned that AWS is more scalable PaaS and it terms of wide range of tools and platforms ready for use. Adding to this, OpenShift has the advantage of building private cloud setup for those still struggle with Public Cloud regulations .. So I would recommend AWS PaaS and identify carefully your needs to apply the best choice setup and avoid waste resources and paying extra subscriptions for not well utilized sources.

As per my personal experience, AWS is a very scalable Platform as a Service making it useful for all sizes.AWS provides many failover models which may be difficult to understand in terms which suits your requirement. Be sure to understand your capability needs and discuss with AWS these different choices.