note: This is a highly technical topic. None of these will be stable for a few years yet. There is a lot more to say and discuss, this is just an optimistic overview.
New APFS will have many benefits. Most of them will be under the hood, end-users will benefit from them but won't really notice a difference in their workflows. The ones you
will notice are these:
Your data will be a lot safer in the case of crashes. Data loss because of power or crashes will be minimized.
There is
sparse file support. This will make virtualization much better, file system will be faster and backups will be smaller.
Faster encryption. There is native support now.
There is snapshots now.
HFS+ (the file system Apple uses now) is 20 years old and full of patches to support modern features. It is, essentially, a hack. APFS is a modern file system in every sense. It should improve almost everthing related to SSDs, which is actually almost everything. Apps will launch faster, data will be copied and written faster, directory sizes will be determined almost instantly, it is optimized for soid state so drive lifetimes will be improved.
All in all, this is a great improvement. It won't effect iOS that much, but you will definitely feel it with macOS. They are testing it first with iOS, because it is controlled. Apple control everything that goes into it. So, don't jailbreak.