There are couple of things we need to consider first to answer your question:
1. APFS in terms of I/O (that is - input-output, read and write data) focuses on improving foreground apps and tasks. It is reasonable to think that background tasks can wait a bit longer to read or write data they need.
2. It doesn’t make processor or graphic processor to handle more task or make them faster.
3. Apps are multithreaded - if app is made along Object-C or Swift guidelines - UI - user interface - is main thread and background tasks are secondary thread (i.e. on slow connection the app you are using downloads data, but user interface is still responsive and probably shows some indicator that data are being downloaded, you can easily switch from one tab to another).
4. Open/save file: with APFS it is possible to do atomic updates - which mean: app is saving only changes to a file or load from a file only things that have changed, not the whole file.
With all that considered: performance gain with APFS would be from reading data needed by foreground app first, using less bandwidth (connection between CPU, RAM, and flash memory) while loading and saving data, postponing some disk operations that are requested by background processes.
To sum it up: you should see some improvements in situations like scrolling through conversation in imessage, saving changes to modified picture, opening files.
(Obviously, sorry for my lousy english, it’s not even my third language)