Something I had to first look up because I keep forgetting what the color space is called.
Supposedly, you can choose between RGB and YCbCr color formats for HDMI output, with YCbCr being the default for HDMI connections. How do you choose? Good question, as I've never looked it up.
That's the main difference. HDMI on the mini can handle up to a 4K, 60Hz output. Plenty of bandwidth for a good monitor. But it's the color space that's important here. Computer monitors expect RGB data. When you use HDMI, RGB has to be converted to YCbCr (TV color) before being sent to the monitor. Not that the very few milliseconds per frame it takes to do this is anything you'd notice.
It's also why HDMI to DisplayPort, or HDMI to USB-C cables sometimes don't work. The computer and monitor are then both confused. Are you trying to get RGB, or YCbCr color? Which again, is something better quality monitors can handle, but is also still not a preferred choice.