Pretty similar. The main difference from the architecture standpoint is that Enterprise DC/OS uses Mesos+Marathon for container orchestration and OpenShift uses K8s. The other functionalities are mostly overlapping.
There is also an OSS version of DC/OS minus some security features. Also, historically Mesos has had better support for running stateful workloads but K8s is catching up too.
Recently, DC/OS announced support for K8s too which is similar to the K8s announcement from Docker.
I've not look too much at Mesos and DC/OS, so could be wrong, but my understanding is that where Openshift is focused on managing containerized workloads using Kubernetes and Docker or CRI-O , Mesos and DC/OS are more widely focused on managing a variety of workloads which could include containers but also VMs etc.
For me, the benefit of Openshift over vanilla Kubernetes is the additional management tooling and the strong default settings for production use.
Openshift has a lot of focus on things like manageability and security which make it well suited to production workloads in enterprises and anecodotally it seems to be taking off quite well in enterprise customers.
There is also an OSS version of DC/OS minus some security features. Also, historically Mesos has had better support for running stateful workloads but K8s is catching up too.
Recently, DC/OS announced support for K8s too which is similar to the K8s announcement from Docker.
Disclosure: Apache Mesos committer.