The Auduino is a micro controller where a Raspberry Pi is a micro computer.
These may not seem different but they are, for example a micro computer can run a operating system such as Linux while a micro controller has only one set of instructions to perform over and over again.
Both designs are legacies of the early days of computing and what is means to say what a computer is.
Two ideas that define what a computer is came to be called the Harvard design and the Von Neumann design.
The Von Neumann design is used in all modern computers such as a desktop or laptop. They use a medium such as a hard drive to store information and RAM chips that are used over and over to complete different task.
For example, a desktop can not only surf the Web but can also be used to run other programs form tax software to drawing programs.
The Von Neumann computer design is much more versatile since it can complete many different task often at the same time.
The Harvard design is much more simple it uses non-volatile memory to complete only a set task over and over.
An example of this, is a car computer that only needs to complete the same set of instructions over and over with no need to do other task. Christmas light displays are another example where a micro controller is good.
Both models are used depending on the task that needs to be done. A machine that welds the same spot on a car all day long in an assembly line doesn’t need lots of software such as a operating system than another program for instructions. It simply needs a minimal set of instructions to complete over and over.
Raspberry Pi
The Raspberry Pi very much follows the legacy of the Von Neumann design like any modern desktop or laptop does.
It can load and run an operating system, such as Linux or Windows 10, and can run programs on top of the Operating System to carry out its instructions.
The newest version of the Raspberry Pi is a quad core 900 MHz ARM processor with 1 GB of RAM.
As far as hardware goes this hands down beats the Auduino when it comes to hardware.
Auduino
The Auduino uses a 16 MHz processor that compared to the Raspberry Pi is ridiculously slow.
But again it depends on the job that needs to be done that separates the Auduino from the Raspberry Pi.
Micro controllers can be compared to micro computers like a car vs a tractor. A car is much more versatile and can carry out more task from going to the store to going to work while the tractor can be used to plow a field day in and day out with no need for the versatility of a car.
The idea of a micro controller is why build some complex expensive project when all that is needed is a simple board?
Why own a Ferrari if you can only ever drive it in a city?
Both have their place depending on the job that needs to be done and how the architect of a project wants to build the project.
Summary
Both the Raspberry Pi and Auduino are good at what they do. They can do amazing things depending on the creator and what task need to be done.
If you simply need a control board to setup a display of Christmas lights an Auduino can do this simply and easily.
On the other hand if you want to run a Home Media Center and stream movies to your TV than a Raspberry Pi would be the one to pick.
For simple projects it is best to use an Auduino while for more complex projects the Raspberry Pi would fare better.