I just recently upgraded to a 4K TV with HDR capability, my first. My previous TV was 12 years old and had nothing "smart" on it, as in no WiFi or ethernet, therefore no apps. Basically it was a dumb TV, but one with a really good HD picture. My new TV is a Sony Bravia XBR49X800H, and it replaced the older Sony Bravia whose model number I can’t remember.
Now to the Fire TV Cube and TV 4K. Both are the latest high end models from their respective companies and both are very good devices over all. I own both and I had both connected to my old "dumb" HD TV. I think the TV 4K produced a bit better video on that old TV, but not by much. However, I favored the Fire TV Cube 2nd gen. for its ease of use and general functionality, and much better remote. Yep the TV 4K remote sucks. Bottomline, you will likely be happy with either device as they are both top notch.
I have now connected the Fire TV Cube and TV 4K to my new Sony Bravia 4K HDR TV. The newer TV has the Android TV smart TV system built in and so I can also use that to view Prime Video, TV programming, and all the other apps from which I stream. The Android TV (version 11, I think) is not bad, it is actually pretty good, but I like both Fire TV Cube and TV better, so I’ll stick to comparing those two.
Although the Fire TV Cube was my favorite on the older HDTV set, it does not seem to produce as good HDR results as does the TV 4K on the new 4K HDR TV. the Fire TV Cube does have HDR10 and other formats and it has Dolby Vision (DoVi), but that latter is available only on some selections. For those who are new to HDR, Dolby Vision is considered the best HDR format available on most TVs in my price range. HDR10 is good, but it is not nearly as good as Dolby Vision, according to most reviews I’ve seen and my own experience. YMMV of course!
Here is why I favor the TV 4K over the Fire TV Cube on my 4K HDR TV. Most streams are not 4K, so they don't have HDR as such. Most streams today are still either 720p (cable TV, some streaming apps, and some OTA) or 1080i (some OTA, some steaming apps). These lower resolutions have to be up-converted to 4K for a 4K TV. So your TV's mileage may vary here as some TVs do a better job than others. Mine does pretty good at this. But regardless of the streaming resolution, the HDTV streams are SDR (standard dynamic range) and not HDR (high dynamic range).
Dynamic range basically deals with how much light an image or video or our eyes can see or display. Digital images and video usually have a lot less range in light that they can capture, so the SDR images will either look okay in bright areas and too dark in the shadows, or they will look okay in the shadows and blow out the whites. HDR allows the extra range of light to be incorporated into the image/video, so that shadows have more detail in the dark areas while the bright areas retain color and detail without blowing out the whites in too bright of an image. Our eyes can see a greater range in light than most digital cameras and video cameras. HDR has to overcome that with technology.
So back to watching a 4K TV with the Fire TV Cube and the TV 4K. Both can produce good HDR. The Cube is restricted, or so it seems, to using whatever HDR format the video has. SDR will not have an HDR format, so none will be used when displaying the HDTV streams. However, the TV 4K will use the Dolby Vision HDR format for virtually everything, if you choose to use it. The result is that colors seem better and if the video has HDR capability then HDR seems better, to my eyes anyway. Again YMMV! On the TV 4K, even live TV streams through apps like Philo and Sling TV, etc. can use Dolby Vision (it is the default unless you change it). All the apps I’ve tried including Netflix, CuriosityStream, Discovery+, Philo, Sling TV, etc. can use Dolby Vision regardless of whether their content is HD SDR or 4K HDR or everything in between.
It is the TV 4K ability to use Dolby Vision for all streaming that makes me choose it over the Fire TV Cube 2nd gen. because this gives me more picture adjustment capability than I have on the Fire TV Cube when viewing non HDR streams. Dolby Vision is a premium format, and I much prefer it to the SDR formats as well as HDR formats. So the capability to use Dolby Vision for every stream (SDR or HDR, HD or 4K) on the TV 4K as opposed to only on some 4K HDR streams on the Fire TV Cube makes all the difference to me. One last time, YMMV!
a couple last thoughts. The Android TV built in to my 4K TV only allows Dolby Vision for some 4K HDR streams just like the Fire TV Cube. I still prefer using the Fire TV Cube for some of Amazon's Prime Video content when that content uses Dolby Vision as the HDR format. The picture quality will be about the same on both devices when both have Dolby Vision enabled for the content. But when the Fire TV Cube content doesn't have Dolby Vision enabled, which is more often than not, I prefer to use the TV 4K so I can use Dolby Vision.
Sorry that this was so long winded, but I thought it might be of some use to others. Until I bought my new 4K TV I had never explored HDR for video. I use HDR in my night sky photography, so I knew what it was and how it can greatly enhance a photo image, but I wasn't up to speed on HDR and video since I had no way of viewing it. Hopefully my learning experience with video HDR and my comments thereon will help you understand it a bit more if, like me, you are new to it.