In this instructable I will go over the major differences and show you what the different boards are best at.
Step 1: A Quick Understanding of Both Boards
The Arduino is an amazing platform to use when prototyping because of its great micro controllers and its integrated programming system, it would be fair to say that the Arduino is good at driving motors but it doesn't stop there the Arduino boards can receive and send data to or from pretty much any sensor or device.
Step 2: Understanding the Raspberry Pi
4 USB ports
40 io headers
It also doesn't take someone with a master is computer science to understand it, in fact it's not that different to a computer (in terms of ports or GUI) featuring:
A Hdmi port
And a micro USB port to power the whole thing
When you buy the raspberry Pi alone you will find it it in a neat little box with no cables or add ons, not even a SD card with the os on it, so to get started you will have to get yourself a micro sd card, go to the raspberry Pi store and download one of the free Linux options that work best for your project.
Step 3: Understanding the Arduino
there are many different Arduinos out there that do different things, some have lan ports for connecting to the internet others have tons of io pins, the best Arduino for your project is a whole different instructable.
Step 4: The Conclusion, Which Is Best for Your Project
The raspberry Pi has far more processing power with its ARM micro processor meaning it would be better for projects that may require a gui (graphical user interface) or a connection to the web (like a server) or even for learning about code on the machine that you are programming.
So for my final conclusion let's make two examples of times I might need one of these boards.
First: my school wants to put up a display screen that shows students a calendar with all the school events on it, I'm pretty sure the raspberry Pi wins this one because of its gui and its capability to run apps
Second: I want to make a Bluetooth controlled rc car, it will have four motors, five LEDs and a Bluetooth module that takes up a lot of pins, the Arduino is definitely perfect for this one because of its strong io being able to drive the motors and its many io pins making sure everything can connect and last its low power consumption making sure you can play for longer
Thanks for reading guys and as always if you have any questions please leave them in the comments and I'll try my best to get back to you.