KVM is better. But let's just look at the software instead of judging.
Hyper-V was a free solution from Microsoft to virtualize Server or Client OS as it is a feature on Windows Server since 2008 and came in Windows 8 as well. Free because they had a special SKU dedicated for virtualization called Hyper-V-Server. It had a limited footprint through a core installation (no GUI) to minimize updates it would need.
But that was until the Windows Server 2019 release. With the new release line named "2022", they dropped that SKU altogether. Microsoft now proclaims you should use their Azure-Stack-HCI solution which is a paid offering with a subscription. That in itself is no bad thing as it would work pretty well (did not try myself but read about it). Alas, you will have to pay for that.
Another downside of Hyper-V is the management capabilities and requirements: You have to use Windows to manage that (which you probably already use anyway) but you have to use at minimum the same OS version your Hyper-V is running on. So if you have Hyper-V Server 2016 you have to use Windows 10 as a minimum (expect to have the same feature built as the server 1607).
On the other hand, there is KVM free on most (if not all) Linuxes. There are even free offerings like Proxmox VE with a full package to use it as an appliance, manage through a browser, and such. Way more straightforward than Hyper-V. Citrix Xen Server is also a great solution to get you started with virtualization.
Commercial solutions are also out there to deliver to more production-inclined needs. One is Nutanix AHV which uses KVM at its core. See my article about that for more information.Personally, I used KVM in private projects and some test scenarios at work. We use AHV at work and it is perfectly running there.
I also have a Hyper-V running with a few VMs for a small shop which works great. You have to settle with some limitations but I will switch that away from Hyper-V because of that mess they made with 2022 (I don't want to pay for a thing I have used for free after 10 years. besides said shop is a non-profit). I'm just waiting for the next hardware refresh.
So yes, I think KVM is better and not only because it is still free.
One of the best things about Proxmox VE is that it is open-source and very inexpensive. You get all of the same features as with the more well-known products. Proxmox VE is very easy to deploy - it can run on anything. It is extremely scalable, stable, and very user-friendly. Proxmox VE allows users to easily create virtual machines. It is based on Debian Linux, using KVM.
Proxmox is a young solution and there are still some bugs to work out. When you need technical support, there is a cost, and this can add up quickly. There are some things in Proxmox VE that need a command-line interface. We think it would be better if it were more a web-based interface.
The initial setup with the Hyper V is very simple. It is a Microsoft product so it works seamlessly with all Microsoft products, and does very well with other solutions as well. The Hyper V is a great end-to-end solution that has an amazing fail-over feature, which helps minimize downtime and maintain productivity.
Hyper V can have some stability issues; your stack can become bloated easily. The scalability of this solution really depends on the licensing you purchase. If you are looking to scale up or down you will need to purchase the data center license, which can get expensive.
If you are looking for a Hypervisor strictly from a cost of ownership point of view, Proxmox VE is the solution to choose. It has many of the same features as other products at a very competitive price.
We chose Hyper V, as we are deeply committed to the Microsoft ecosystem and we were also looking for some management solutions that Proxmox does not offer. We also found the fail-over feature very important to many of our clients’ needs.