It was never popularly used in a way accurate to the origin of the classification - in the original paper by Popek and Goldberg talked about formal proofs for the two types and they really have very little to do with how the terms began being used in the 90s and 00s. Things have changed a lot with computers since the 70s when the paper was written and the terminology was coined.
So, language evolves, and Type-1 and Type-2 came to mean something else in common usage. And this might have made sense to differentiate something like esx from vmware workstation in their capabilities, but it's lost that utility in trying to differentiate Xen from KVM for the overwhelming majority of use cases.
Why would I say it's useless in trying to differentiate, say, Xen and KVM? Couple of reasons:
1) There's no performance benefit to type-1 - a lot of performance sits on the device emulation side, and both are going to default to qemu there. Other parts are based heavily on CPU extensions, and Xen and KVM have equal access there. Both can pass through hardware, support sr-iov, etc., as well.
2) There's no overhead benefit in Xen - you still need a dom0 VM, which is going to arguably be even more overhead than a stripped down KVM setup. There's been work on dom0less Xen, but it's frankly in a rough state and the related drawbacks make it challenging to use in a production environment.
Neither term provides any real advantage or benefit in reasoning between modern hypervisors.
