@Lumpkin
It depends what you want to do with it. The Arduino runs in real-time and has lots of inputs and outputs which means it's suitable for controlling circuitry and suchlike. The Pi is like a very small PC, although it runs on a different architecture. It doesn't have as many I/O pins and, though it
can run in real-time, it's not designed for it, so it isn't really suitable for controlling circuitry. However, it is more powerful, so if you want to do more complex computation and you only plan to use peripherals with standard connectors (USB for input, HDMI or S-Video for video and 3.5mm line-in for audio) then you should get the Pi.
However, my recommendation is not to get either. There's a secret third option: the BeagleBoard BeagleBone Black, which is kind of like having both except easier, cheaper and smaller than having both. It has the microcontroller capabilities of the Arduino with the power of the Raspberry Pi. It might even be more powerful. I think its CPU is faster, at least. And I think it has more I/O pins than the Arduino Uno while being more powerful and only slightly more expensive. Plus, since it boots a full Linux distribution, you can write software in whatever language you choose, as long as it has an ARM implementation.
http://beagleboard.org/products/beaglebone%20black