I think you can get summon the biggest differences between the two:
- Hyper-V runs on almost any hardware and you can keep current with the software without changing you hardware for quite a long time
- ESXi is quite pesky at the hardware it runs on - and you can be quite assured, that the newest version of ESXi will not run on any server older than 3 years. That is the biggest disadvantage of ESXi in my opinion
- Hyper-V is very pesky at the VM Guest software you are running under its hypervisor and if you need a graphical console other than RDP on your VM guest, the graphic is really bad - further there is no real support for USB (pass-through) devices. That are the biggest disadvantages of Hyper-V in my opinion.
- ESXi supports a multitude of VM Guest software and you can even run quite old guests easily, it has a really good graphics performance and it does support USB-passthrough for almost all available USB devices
- Hyper-V is Windows, so you can use a multitude of software for all sorts of jobs to be done including management of the hypervisor, but the included management tools are quite limited in my view
- ESXi is quite proprietary, so the software options you can run on your server are quite limited, but the included management tools (if you are using Vcenter server) have much more possibilities (they are only horribly slow, if you look e.g. on the webclient)
The rest is of importance only for very specific or big environments IMO.