This comparison will be largely moot if and when the 2018 iMac refresh brings the 21.5" iMac range to Retina 4k screens across the board and quad core desktop CPUs across the range, but even if it didn't the 2017 iMac base model is already stretching the value argument against the current 2014 Mac Mini.
Let's discount the base Mac Mini for the moment - it's comically underpowered and even upgrading the RAM at Apple rates is ridiculously pricey with High Sierra and probably Mojave requiring 8Gb base more than ever.
A US mid-SKU 2014 Mini gets you a 2.6GHz 28w TDP i5-4278U with Iris Graphics 5100.
A US base-SKU 2017 iMac gets you a 2.3GHz 15w TDP i5-7360U with Iris Plus Graphics 640.
For equality, both models come with 1Tb HD and 8Gb of RAM. Both are nominally not upgradable after purchase.
The Mini costs $699. The iMac costs $1099.
For your $400 extra, you also get a 1080p non retina display with front facing webcam and microphone. You get wireless Magic Keyboard and Magic Mouse 2 as well (each worth $99) and a Lightning to USB cable (with $19). You also get Thunderbolt 3 on the iMac which you can attach fast storage but also an eGPU if you feel you need more compute power but the costs associated with that will increase massively but you'd at least officially have the option.
OK, so forgetting that some of us prefer to bring our own keyboards, mice or monitor on a head to head basis the iMac has a more powerful iGPU with a CPU that has a higher geek bench due to being more modern despite the lower TDP. Modern heavy duty benchmarks might reveal more nuance there but we are looking at single core geek bench of around 3200 vs 4400 and multicore of 6800 vs 9200 for old vs newer CPU.
For comparison, the i5-8250U has single core of 3642, multi core score of over 11k while the UHD620 graphics falls somewhere between the Iris Plus 640 Graphics and the Iris 5100.
If you are that serious about bringing your pre-existing peripherals you can sell the keyboard and mouse and perhaps invest in a Thunderbolt adaptor for your pre-existing screen to run a 2 screen setup to close the gap up a bit.
If you prefer a headless setup or need the space then we have slight issues that could be mitigated with the purchase of a MacBook Air which starts at $999 but you'd have to buy a customised mini with all SSD making the comparison a bit trickier.
And if you paid $1299 for the mid SKU iMac 2017 your extra $200 buys you an upgrade to a Retina 4k screen at 4096x2304 P3 display, 3GHz desktop class CPU (geek bench 4k single score, 11k multicore) with 4 genuine cores driven by a Radeon Pro 555 GPU.
So in total, your extra $600 over the mid model Mini gets you a 4k screen with webcam and mic, Radeon 555 GPU without needing an eGPU, wireless keyboard and mouse, and lightning to USB cable. Imagine this with 6 desktop cores and upgraded GPU later this year...
We could repeat this comparison with a MacBook Air if we start to spec SSDs up on both units but the sad truth of the matter is that Coffee Lake CPUs will completely exterminate the 2014 Mini on benchmarks if and when they arrive on the 2018 models owing to the extra cores that they bring.
Basically by the time Coffee Lake arrives on the other Macs the Mini (and the MacBook Air for that matter) really needs to be involved in the upgrades or there's a serious danger that they'll be overshadowed by more powerful PCs - never mind Macs.
