Back in the old days, I used my C64 for word processing, printing sheet music, a bit of solving mathematical problems. I have never owned a modem, so I couldn't call BBSes, but my big brother did one fateful summer. It was me who found the modem hidden beneath his bed...
The 128 has a native 80 column mode for even better word processing, spread sheets, simple database software and so on. It also has more memory and a 2 MHz processor so in theory it should be more powerful. As always, it is a matter of available software. A computer is never weaker than its software.
Nowadays, you can get one of a bunch of Ethernet interfaces and get connected to the Internet through Contiki or any other software. You can get memory expansions, turbo processors, hard disks etc, but the practical use may be limited and won't compete with what you can do with a 386 PC or better.
Are you asking if there are specific, non-gaming tasks where the C64/128 is preferred over all other vintage and perhaps non-vintage computers? I'm not sure if there are any such tasks. Perhaps it is handy to use as a programmable video display device, some infostation controlled by a custom device in the joystick port. Again, it is far fetched.