Xen is an external hypervisor; it assumes control of the machine and divides resources among guests. On the other hand, KVM is part of Linux and uses the regular Linux scheduler and memory management. This means that KVM is much smaller and simpler to use; it is also more featureful; for example KVM can swap guests to disk in order to free RAM.
KVM only run on processors that supports x86 hvm (vt/svm instructions set) whereas Xen also allows running modified operating systems on non-hvm x86 processors using a technique called paravirtualization. KVM does not support paravirtualization for CPU but may support paravirtualization for device drivers to improve I/O performance.
