Chris has explained it pretty well.
I see the Raspberry Pi as being a computer - a small computer (and now fairly powerful with the RPi 2) that is capable of doing a lot of physical computing. Using sensors, LEDS, relays, motors etc etc.
If you want a "clever" device to run these things then a Raspberry Pi is good for that. It has a full operating system, networking, can use USB devices (webcams, storage etc). Fairly low power too, especially the A+.
I see the Arduino as being a "simple" microcontroller. They're very very capable devices and they're great for similar things to the Raspberry Pi but without any networking with the cheap Arduinos and much less clevers. I'd say they are more reliable for certain things, I wouldn't ever expect an Arduino to crash/freeze etc (unless the code was rubbish) but a Raspberry Pi is more liable to have issues because it runs on a bloaty OS (in comparison). Very low power compared to the RPi.
When you pair the two you can have quite a powerful setup for physical computing, automation etc.
The preference would depend on what you want to do.
Arduino is cheaper - I price them at about £2 per board (on ebay from China), cheap enough to make them pretty much disposable in my eyes.
EDITED: 4 Apr 2015 19:54 by ANT_THOMAS