See the wiki pages about PVR
http://kodi.wiki/view/PVR and more specifically checkout the wiki page about "PVR backends"
http://kodi.wiki/view/PVR_backend which have an "Other" section with compatibility tables.
HDHomeRun (SiliconDust), VBox TV Gateway, Dreambox/Vu+ (Enigma) and Octopus NET (Digital Devices) are all different types of boxes which all have integrated TV-tuners.
As far as I know however HDHomeRun is the only one that makes boxes for all types of worldwide digital broadcast systems, while I think that the others only make "DVB" boxes for EMEA (and maybe APAC) regions.
Unlike the HDHomeRun series the boxes from those other manufacturers also works as classic TV-boxes does so they have HDMI output ports and remote controls.
That is, the other boxes are really only classic TV-boxes that also work as network-attached tuners, while the HDHomeRun series are dedicated network-attached tuners with no HDMI output port and remote control.
The other boxes could be called boxes that are "Jack-of-all-trades but master of none", but the HDHomeRun series is master of its specialist field.
You can not connect a HDHomeRun series directly to your television as it has no HDMI port, only a network port, so you have to access it through Kodi or if you have a Smart TV install a client app for it.
Benifit of using Kodi with any network-attached tuners is that you get all your media including live television in one app.
Another tip is to buy an "Android TV" based Smart TV, as then you can run Kodi as well as other HDHomerun client apps directly on the TV.
https://www.android.com/tv/
Recently HDHomeRun also got native support in Android TV 7.0 officiail Live Channels app, but unfortuatly not many manufactuers ship Android TV 7.0 for their Smart TVs yet, however read that Sony will soon though.
https://androidtv.news/2017/02/live-chan...r-support/
You can read more news about Android TV related topics on androidtv.news
https://androidtv.news/