Xen can implement things like a CPU scheduler exclusively focused on VMs, while KVM has to deal with the normal Linux scheduler for processes.
Xen can do advanced defense-in-depth techniques like driver domains -- something impossible to implement on KVM.
Xen has a mature security response process; if you're a cloud provider, or ship anything with Xen inside of it, you can be notified of security issues typically two weeks before the public disclosure; and we're quite thorough about what we issue security alerts for. For KVM, you just have to hope that your functionality is worth issuing a CVE about, and unless you're a distro, you're only going to be told after it's been made public.
Xen is a microkernel, so you can run it on tiny embedded devices for which Linux / KVM would be too big. Xen is small enough that it's actually feasible to do Functional Safety Certification on it.
That's why Xen is still used by QubesOS, the NSA, and various defense contractors; why a number of cloud providers (including say, Ghandi.net) use Xen; why Xilinx has their own Xen distribution; and why Xen is in the reference implementation for ARM's automotive stack -- in addition to being officially supported by SUSE, and being the driving engine behind Citrix Hypervisor and XCP-ng.