Depends what you mean by "more than VM handling". VMware handles everything you could possibly think to do with VMs and many you probably never thought about. For example: Scripted live migration. Single click to deploy a test network of VMs. Virtual desktops. Wrap up a VM in a single file that can be "played" remotely. Scan all your VMs for vulnerabilities.
Beyond VMs they attempted to branch out into containers with a version of Kubernetes (VMware Tanzu) which I believe didn't get many sales.
The competition are roughly:
- All the cloud providers
- oVirt (formerly Red Hat's RHV, probably the closest thing to vSphere in terms of UI and deployment)
- Kubenetes + Kubevirt
- Openstack, probably
- Virtuozzo
- Virtual Box
- Proxmox
- Nutanix
- Single node installations using things like virt-install
- Rolling your own management on top of KVM or Xen (surprisingly popular but I wouldn't recommend it myself)