Sort of.. Xen/Xenserver are different
Xenserver is built on Xen, and is pretty much a turnkey product as long as you like the way it works, not unlike ESXi in many ways. It's also now open source (except for, yes, VDI bits and a few other things)
Xen itself is a tad different - it's the base hypervisor, and sometimes a bit of an arse to get going depending on what you're doing with it. You can tweak it at a fairly low level, though, which has its advantages, as is the fact it can work with just about any (x86, arm) Linux distrubution, NetBSD x86 (does a few things better than Linux, others not so well) and Solaris (never tried).
However, it's a solid product and the design is mostly good. KVM is better and faster at a few things (PCI passthrough, for one), but doesn't seem to hang together quite as well - it's basically an (optional) qemu accelerator with a (rather good) vfio addon for hardware passthrough, rather than a bare metal hypervisor with a coupled host OS that drives devices.
Just don't be tempted to use xen -unstable if your favourite feature of the day isn't around yet, you're likely to regret it. Specific, tested xen releases are fine, and if included in your distribution much easier than compiling from source.
ESXi is bloody fantastic *if* all your hardware is supported, your network is perfect, nothing needs to be tweaked and you don't need to also use the glass console of the ESXi server. The problem comes when it doesn't work, the management tools decide not to play ball, or the next version with a killer feature is released, and it decides to kill off support for your motherboard/network card/raid controller for no particular reason other than because they can't be arsed to support it. In that case, just buy the new hardware - do *not* try and hack it to work.
For work usage, I'd consider ESXi on nice certified hardware, Xenserver or at a pinch RHEL with KVM. For home, if VMWare Player/Workstation isn't sufficient and ESXi is overkill, I'd go for KVM first, then Xen.