Yes that is pretty accurate. The difference is that Vmware is further along in revenue, and has already leveraged their position in compute to diversify into adjacent markets (storage and networking). Red Hat has failed to do that.
And of course Vmware has already been integrated into EMC years ago, quite successfully. Although you could argue the ongoing Dell/EMC saga could jeopardize that... Depending on how well you think it’s going.
However Pivotal CloudFoundry is not their best-seller... I doubt it’s even in the top 5. Vmware’s empire is built on Vsphere/esx (their core business) and, more recently Vsan (storage) and NSX (networking). The former is the largest. The latter two are the fastest growing.
Container platforms are a relatively new category, so sales are not huge. In that category Cloudfoundry might be slightly ahead, but I think Openshift has more momentum because their early bet on Docker then Kubernetes is paying off. Pivotal has PKS but it feels half-hearted.
Pivotal is a separate entity and business model from VMWare, I wouldn't compare them directly. They are both owned by EMC/DELL.
I'm under the impression that cloud foundry is specifically targeting mega corporation like fortune 100 banks. In that context, it only takes a few sales to capture the market and a lot of money.
And of course Vmware has already been integrated into EMC years ago, quite successfully. Although you could argue the ongoing Dell/EMC saga could jeopardize that... Depending on how well you think it’s going.