I have some experience on the topic that may be useful. Not with Eizo ColorEdge specifically, but with a similarly specd professional monitor. Anyway, the monitor is the less important part here, as long as it's good.
DP allows to use 10-bit colour, but it doesn't mean it will automatically. (At least on a Windows PC). All of the video card, its driver, and, importantly, the software you work with must be 10-bit aware. It's no use to have 10-bit hardware if the software still decodes colours in 8 bit (as most do).
Typically, 10 bit support is disabled by default, providing the most compatible 8-bit output. In order to enjoy 10-bit colour, you need (apart from the cable):
- Open the video driver settings and find the respective setting there, and enable it. Obviously this varies with the driver. If it worked, the screen should flicker as if you were changing the resolution: this is a new mode. Professional monitors such as Eizo will actually display that this is a 10 bit mode.
- In your editing/viewing software, try to find a similar setting and enable it. This varies even more, and in many packages you won't find it. Here are example instructions for Photoshop.
But if the software doesn't support 10 bit, does it make any sense to enable 10 bit in hardware? Possibly. Potentially, if the software engages the OS's ICM engine (colour management), the OS has the cabability and knowledge to engage (at least) 10 bit colour conversion. But it's hard to verify this.
Is there an actual difference in quality when everything works correctly? Yes, but more often than not you need to look for it and compare before/after. Normal untrained eyes will almost never see it. Gentle clean gradients have the most visible improvement. But on most 'normal' photos you'll be very hard pressed to find the difference (not to mention that a 'normal photo' is jpeg, which is only 8-bit).
But there is a flipside as well. There may be issues that can degrade the image quality.
The first issue are software bugs. Not that many people actually use 10-bit output, and the code that deals with it may not be as perfect. I didn't have noticeable issues with editing software, but nVidia drivers had a horrendous bug at some point which caused it to use 6-bit (!!!) colour after a reboot when 10 bit were selected previously. This can easily go unnoticed for some time.
The second potential issue arises if the cable quality isn't particularly good. With 10 bits, you are using more of the bandwidth, which is limited. If you are near the capacity (which for DP is, admittedly, fairly high: about UHD (4K) @ 60 Hz), you may have signal quality or stability problems at 10 bit which don't appear at 8 bit.
The third problem is DP-specific and is totally different, and doesn't affect everyone. When a DP-connected monitor turns off, it drops out from the OS, which often wreaks havoc on the desktop, if the computer is still on. This is super annoying for scenarios where the PC is used as a server and never turns off, using remote desktop connection for administration, and the monitor is used periodically. In the olden times, the computer could detect the monitor correctly even if it was completely off: a special circuitry was placed for that and worked even over the analog VGA cable. It could still work over DVI, and many (but not all) monitors support this over HDMI. But DP, apparently, can't support this. This is a great pity and my main objection to DP.