What is more benficial for the Xbox One X? HDR or 4K

First of all, let's remove the Freesync feature from the equation. That only applies if you connect these monitors to a PC that supports this feature.

The next item is that it seems this is a PC monitor you are looking to get. The reported resolution from the monitor is fine for when using a PC, but when you hook up the monitor to an Xbox One X, you will only get "standard" TV resolutions out of them.
What I mean by that is that you'll either get 1080p or 4k resolutions but nothing in between. In other words, if you get the 4K monitor you'll be able to display both 1080p and 4K video, but on the 2K you are limited to 1080p (since 2K is not a valid TV resolution)

HDR is related to the Color representation on the screen. With HDR you get a wider range and color gamut because the panel can display brighter colors as well as darker colors without saturation of nearby pixels or making them darker. Now, it appears as
if the only way to enable HDR using TV resolutions is via 4K, so if you get the 2K monitor you'll not get to use the HDR function.

With the above said, I recommend you get the 4K monitor as that gives you more flexibility and you;ll be using the features of the monitor fully while on the 2K case you'll be wasting them as you;ll never get max resolution of 2K on it and no HDR.

Hope this helps.

I don't think HDR will activate if the resolution isn't set at 4K. The
HDR page about the Xbox One S seems to imply exactly that, and there is currently no support documentation (afaik) about the Xbox One X in particular.

you need hdr for 4k output

Actually, you don't.

Uhd and hdr are required for 4k output

You need UHD, in the sense that you need the TV to support 3840 x 2160 resolution, but you don't need HDR enabled to reach 4K. UHD 4K is the amount of screen resolution available measured in pixels, HDR is the ability of the TV or monitor to display more
natural colours.

Note that the Xbox One S can do HDR in games that support such a feature, but regardless of what resolution you set, all games max out at 1080P internally. If the display is 4K, it will remain in 4K, but games will only be upscaled. Only the Xbox One X
can play Enhanced titles in 4K natively.

You should be able to disable HDR, how you disable it depends entirely on your TV. Disabling HDR via the TV settings should not disable 4K screen resolution. Indeed, some Xbox One games do not support HDR, Fallout 4 on the One X can play in 4K for instance,
but it does not support (or indeed have an option for) HDR.

On my Sony Bravia Android based TV, I had to go to the main settings and enable HDR functionality. Even then, I had to set the HDR setting to 'Auto' on the HDMI port I have my console connected to. If you have HDR set to 'On' all of the time, non HDR games
will display the wrong colours, look oversaturated. With 'Auto' enabled, HDR will only operate when it detects an HDR supported game. This may not be a feature of your display however.

What make and model is your TV?

I like using my 65" Samsung 4K with HDR and my 50" Samsung 4K with HDR. I mainly play games on the 50" with my Xbox One X. More Netflix and movies on the 65" with my Xbox One S.

Hello Slash,

In addition to the information requested above, please check out a couple of our links involving troubleshooting 4K on Xbox one:

Troubleshooting 4K and HDR on Xbox One X and Xbox One S

What is 4K?

Hope this helps!