I always viewed Arduino as a prototyping platform. Once you finalize your design, you'd buy a $2 AVR and stick it on its own circuit board with its own components, freeing up the Arduino and any shields you have for your next project.

That is quite different to the Raspberry Pi, which just appears to be a small, cheap, general purpose computer that comes without a case.

There is certainly some overlap, but I'm not sure they are directly competing with each other.