Well, HFS is a very old (33 years old) file system. It dates back to 1985, and has seen a major revision in 1998 (HFS+).
This is a very good article (2016) from the point of view of a ZFS developer (for some time it was rumored that Apple will adopt ZFS as an HFS successor):
The article also explains shortly why a HFS successor was overdue, but above all it describes in a pretty readable way the advantages of APFS (and it critically also points out the shortcomings, as least as of 2016).
IMO, one of the major improvements of APFS is the Snapshot feature.
There is already backup software (for example ChronoSync 4.9, which I highly recommend) that makes use of Snapshots.
This should help for example to create reliable boot clones of the start volume: At the start of the sync progress the program makes a snapshot of the source volume, and then when anything changes on the source disk during the sync process, the sync will be done against the file state as per the snapshot.
It seems also CarbonCopyCloner, another good tool, is making use of snapshots. I’m sure in the next 12 months or so we will also see a new Time Machine that makes use of APFS snapshots in some way. (The old/present Time Machine with its thousands of hard linked files and folders becomes a maintenance nightmare, once the TM backup grows fairly large.)
Another big advantage is the improved reliability, well, at least I hope so. Things like the regularly due repairs of the B-Tree should be a thing of the past. (Until recently I had APFS only on the internal SSD of my MBP, for about 16 months, and so far I haven’t seen Disk Utility doing a single repair. I still have to see how the APFS works out on my external hard disks.)
Finally, a big point seems to be the encryption, which is now (APFS) a file-system-native encryption.
Another at least interesting thing is the file Clone feature. It’s not a full deduplication system, from a user perspective it works more like hard links. (But it’s not the same.)
But you really should read the article I’ve linked above…
Concering the “risks of conversion” (which was part of your question), I can’t tell you much. The conversion of four external hard disks was without any problems, but since it’s only two weeks or so that they are running with APFS, that doesn’t mean much.
Later this week I will convert the Fusion Drive of my older Mac Mini, and if I run into any problems, I will let you know.
Just noticed that the Mac Mini already runs on APFS since the Mojave update. Stupid me! See post below.