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I've made some research and now understand that Hyper-V runs alongside the Windows Server (i.e. it is not an in-windows app). Therefore it would be hard to achieve the ESX performance close to ESX or Hyper-V even when deploying on linux. Or wouldn't it? Maybe considering a partition as disk for virtualbox? Idle Linux overhead isn't this much, is it?
In the case of ESXi it's about the clustering, filesystem/network virtualization, management and orchestration for hundreds of servers, disaster recovery, enterprise security/software integrations, and so on. That VirtualBox requires a client OS is just a footnote in the comparison of functionality.