Hypervisor. The hypervisor doesn’t need to know much about application needs. It can perform compression/deduplication for the VM, and you can therefore add more memory to the VM and prevent it from using additional swap and CPU to perform memory management.

The other benefit if assigning more memory instead of using guest compression is that the hypervisor can use a memory ballon when it needs to reclaim memory, forcing the VM to decide what will stay in memory and what will be sent to swap.

The concepts of storage are similar. If you need to encrypt data at rest, it’s usually better to let the hypervisor or SAN handle it. Letting a VM perform storage encryption would work, but would eat up CPU cycles and prevent the hypervisor from performing compression, deduplication, and in some cases knowing what space is used but empty.

Storage compression is similar, you want the hypervisor to handle it since it can compress block of data that are the same across the environment. If you have 1000 machines all running the same OS with many of the same applications installed, then you’ll have a lot of opportunity to save space. You can use these same ideas when it comes to memory.