Is there anything a rotary tool can do that a oscillating multi-tool can't?
A few things I've done/do with my rotary tool that can't be done with a oscillating tool:


Etching numbers/letters with a diamond point (in very hard materials; such as marking serial number/ownership on a bicycle frame or tool).
Polishing; many rotary attachments are made for polishing fine items. 
Routing. There are several router bit setups for roto-zips and dremels for doing very fine (i.e. gingerbread) work. 
Curved work, such as fitting tile or wooden flooring around a small curved spot.


Overall, the oscillators have their uses, and replace other tools, but the blades can be hideously expensive. The bits can be cheaper for a rotary tool, and sometimes they're just better suited for a job -- cutting holes in drywall to fit an electrical box is one great example of a task where you can do it by hand, you can do it with an oscillator or even a reciprocating saw, but once you do it with a rotozip and the right bit you're just going to hate doing it any other way.