Kata Container & gVisor provide approaches to securely isolate containers by keeping them out of the direct kernel space. Kata Container uses virtual machines with lightweight kernels to isolate containers, while gVisor uses a userspace kernel implemented in Go to provide isolation. Both aim to protect the host kernel by preventing containers from accessing kernel resources directly. Kata Container has a larger memory footprint than gVisor due to its use of virtual machines, but provides stronger isolation of containers.