There isn't any direct equivalent to a vCenter; backup by cluster and backup by SCVMM both have certain similarities to vCenter when compared to backup through the individual host. I generally find that adding clusters to the backup infrastructure works best in small to medium environments; adding SCVMM to Veeam can make more sense in enterprise environments. One big difference here is CBT - if a VM is a cluster resource, CBT won't work if you try to back up through the host instead of the cluster, and can fail if there's a problem with any node in the cluster.
You're right that there's no equivalent to the SAN/Hotadd/NBD transport mode concept, nor to the idea of deploying VM proxies. Usually your hosts will act as proxies (meaning that we run data movers on the host to read and compress the VM data), although with some kinds of shared storage you can set up "off-host" proxies.
Low-level backup procedure is very different, but suffice to say that we're using volume shadows on the host rather than using snapshots (checkpoints). However, if you look closely you'll notice that VSS will automatically create and delete checkpoints - this works differently in each OS version. I guess the closest equivalent in our VMware backup options would be backup from storage snapshots.
Application-aware works differently too - our in-guest temporary process doesn't interact directly with in-guest VSS, instead the in-guest VSS is managed directly by the host when we request the host-level shadow copy. There is no VIX equivalent, so AAIP requires a network connection.
Hyper-V quiescence is very different from VMware Tools Quiescence; for VMs that support 'online' backup the only difference between HV quiesce and our AAIP is that with AAIP off, Veeam B&R won't inject a process to gather application and file system data. For VMs that don't support 'online' backup, the results of HV quiesce vary depending on host and guest OS.
There's no such thing as NFS datastores in Hyper-V, so there is no vPower. As a result, Instant Recovery and Surebackup work completely differently (the details are documented in the user guide). This can have some interesting consequences, like this restriction: https://www.veeam.com/kb2028
. Also, there's no Surebackup for replicas in Hyper-V.