I have a minipc with an AMD 8945HS, 96GB ram and 2x2TB storage for quite a bit less than $1400.
But the M4 Pro Mini has a significantly faster CPU, much faster GPU, much higher bandwidth, quieter, cooler.
And while mini PCs can get pretty small, they often come with an external power supply that is half the size of the computer. M4 Mini doesn't have an external PSU, which is a really nice bonus if you ever want to put it in a backpack.
It depends on what you value.
https://browser.geekbench.com/v6/cpu/compare/8794796?baselin...
The minipc can also power off of USB-PD, and many offices will come with hubs or monitors that can deliver 90W on USB.
For 4000€ with just 64GB of RAM instead of 96GB and the same 4TB of storage. So, sure it might be "significantly better" but at 3 times the price that is the bare minimum.
Side question: Lots of mini pcs accept usb-c PD input, i.e. your external PSU can be any laptop charger. Does the mac mini support that?
You can get a cheap external SSD.
But the RAM bandwidth is not in the same class. The 64GB would be a lot more useful than RAM on an AMD chip.