What can be done with a Raspberry Pi but not with an Arduino?

You can think of raspberry pi as a laptop with programmable pins, as well as being a micro-sized computer.

I think we could classify the difference into two categories, a hardware, and a software.

Hardware

For example, and not as a limitation,

1. You can show out graphics and movies after attaching an LCD whether it is big like TVs or a credit-card-size one, in which Arduino cannot do it obviously.

2. Using many features that can not be done in Arduino simultaneously like using Bluetooth, WIFI, Ethernet networking, and USB at the same time, you can do each of them in Arduino individually using a shield for each feature but not simultaneously as most of the shields cannot accept other shields to be installed over it.

3. Its high processing speed enables it to get rid of some circuits like the PWM circuit as it could do it using a simple software code that will not delay the processor much as in Arduino, so you can extend your capabilities even if you do not have the hardware to do it as long as your GPIO pins are available enough, of course, you cannot bypass some circuits like analog reading as it needs a hardware and cannot be programmed.

On the other side

Software

1. You can program the pi as you program your laptop, it is not limited to a certain language like C in Arduino you can program it using different languages including C, like python, java C++, etc. Also, you can install a meta-operating system like ROS for robotic applications that need a direct connection with sensors through pins in some cases.

2. Although Arduino can do multi-threading using FreeRTOS the pi is more reliable and faster it can process images, read sensors, take decisions and command actuators simultaneously.

3. You can utilize it as a web server as you can install an OS on it.