I tested the original case, and it was fairly noisy, like a busy laptop. I don't recommend it.
You may find it slightly cheaper if you install the RAM and SSD yourself. This would be easy with the normal case. Installing the silent case was more tricky, since it requires using thermal paste to connect the case to the CPU.
Same 8GB/128 GB, but probably lower CPU for £307: https://www.amazon.co.uk/dp/B077SLPZ63
There are many different configurations on Amazon/Ebay
But yes, the decked-out i7 Mac Mini is really expensive! As noted elsewhere in the comments (and in the article), a big chunk of that cost is in Apple's 1TB SSD pricing - ticking that option adds $800 over the 128GB SSD for some reason.
A quick glance at Amazon (US) says that a 7i5 NUC with 8GB of RAM and a 250GB SSD is $540.
I'm actually very interested in these - could you point me at some? I've been interested in getting a NUC8 machine, but the cheapest I can find one for (granted, in the UK) is £750 before RAM & SSD... and I have been seriously considering the new Mac Mini as a result because the final price doesn't seem like it'll be much different.
edit: found some on SimplyNUC.co.uk starting at £650 (inc VAT), 8GB of RAM and 128GB SSD, awesome! https://simplynuc.co.uk/8i7beh-full/