The price for the hardware was DKK 2,500 or $400. Synology doesn't have a 3.5" 6-bay NAS, but their cheapest 4-bay is the DS420j at DKK 2300, or around $370. So while that is slightly less expensive and probably uses less power, it also has less room for disks and is significantly less flexible. If you have modest demands and just need something to store your files, it'll work.
Or you could go for the DS1612+ to have room for 6 disks like in my build, which will set you back DKK 6,900 or $1,100. And that uses an AMD Ryzen CPU, not ARM. On the upside, it also has transcoding and media playback functionality like my build, and some features my build doesn't have, like an upgrade to 10gbit ethernet.
I'm not counting disks in these prices, since I used disks I already had, which I would also have done if I had bought a prebuilt NAS.
The TDP for the Celeron J4105 in my build is 10W, representing "the average power, in watts, the processor dissipates when operating at Base Frequency with all cores active under an Intel-defined, high-complexity workload". It very rarely runs at anything approaching a high-complexity load, even when transferring files over gigabit ethernet. It idles at around 30-35C passively cooled aside from the case fans, which run inaudibly at 500rpm.
Obviously the chipset and RAM also draw some power, as do the disks and fans and so on, but it compares very favorably to the quoted 51W under load/25W idle for the DS1612+. That is why I specifically chose a motherboard with that class of CPU.
Let's say the 51W figure is the same for my build and assume a worst-case load, running at full power 24/7. With the current electricity prices here, that's DKK 773 or $125/year.
Compare to the DS420j, which is quoted at 22W, DKK 335 or $54/year, for a device that is significantly less capable.
And my build is not just a NAS. It also serves as my HTPC and couch gaming machine for retro and emulated games, among other things. Plus it's 100% under my control, I get to decide what's installed and which features are enabled/disabled. For me, the choice is obvious.