Pretty much any Arduino can do things like turning on/off motors, reading sensors, etc. The main difference is going to be the number of Input/Output pins.
For example, on an UNO, you can read 6 analog sensors, and you can control the speed of 6 motors (using PWM). If you want to use stepper motors, you’ll need 4 pins per motor, and if you want to control DC motors in two directions, you need at least two pins per motor. Add some LEDs, some sensors, WiFi … and you’ve used up all pins of the UNO pretty quickly.
You could use port expanders, multiplexers or shift registers to get more I/O pins, but it’s much easier to use the Arduino’s own pins (for writing code and for wiring).
The UNO has 14 digital pins (that can output either 0V or 5V, or read the binary state of the pin (either low or high)) of which 6 can be used as PWM. You have to keep in mind that pins 0 & 1 are used for programming and debugging, so these are pretty much useless for other things.
It also has 6 analog + digital pins. These can do the same things as normal digital pins, but they can read the analog voltage present on the pin as well.
If you need more I/O, you can choose between an Arduino Due, Arduino Mega or a Teensy 3.2.
They have much more I/O pins, more memory, and also other features like native USB support (Teensy + Due).
Teensy and Due are 32-bit microcontrollers (ARM, ARM/SAM) that run at 96 and 84 MHz respectively, whereas the Mega is 8-bit (AVR) and runs at only 16 MHz.
The Mega is a 5V board, the Teensy runs at 3.3V but has 5V tolerant inputs, and the Due is 3.3V only.
Teensy 3.2 has 34 I/O pins in total, of which 21 are analog pins, and 12 support PWM. 24 of these are easily accessible through the standard headers. The ten other pins require soldering wires to pads on the bottom.
Due has 72 I/O pins in total, of which 12 are analog pins and 12 support PWM.
Mega has 70 I/O pins in total, 16 of which are analog pins and 15 support PWM.
I like the Teensy 3.2 because it has more than enough I/O for most projects, but not as much as the Due or Mega. Its form factor is much more compact as well, and it fits on a breadboard. It’s a very capable processor, and much faster than a Mega or an UNO. It also has enough memory to drive small displays etc.
A Raspberry Pi is a completely different piece of technology, it’s an actual computer that runs an operating system. It has many times the processing power and memory of an Arduino, and the process of writing code for it is completely different.
Pieter