The importance of I/O pin DC current I am thinking about buying Arduino or Raspberry Pi.  I generally know Arduino advantages (fast start-up, low consumption, ADC converters) and disadvantages (low memory, low connectivity, hard programming), but I simply cannot figure out maybe the most important issue: current output for controlling devices.

One of the common cited advantages of Arduino system compared to Raspberry Pi system is that power per I/O pin is much larger.  Arduino Uno allegedly has up to 20 mA @ 5 V per pin and 50 mA @ 3.3 V per pin making quite substantial power of 0.15 W, compared to say typical 10 mA @ 5 V per pin for Raspberry Pi (although there is no official number available).

On the other hand


this power is far too low to control any motors and you still have to
provide shields,
new version Arduino 101 reduced that current to 20 mA and even less for some other Arduino models.


So, what is really the importance (if any) of these higher currents for home projects, compared between different Arduinos themselves and compared to Raspberry Pi?

There is also a question of total current for all pins together, which is also limited, but it is soooooo difficult to get official limits (for both Arduino and Raspberry Pi).

Please give me some insight into this issue, so I can decide.
The simple answer is: It doesn't matter.

Both Arduino and the Raspberry Pi, and every other common microcontroller board, are designed to control things, not provide power to things.

Digital IO pins aren't designed to drive heavy loads. Yes, some (like the Arduino) can provide slightly more current, but that is really unimportant for most projects.

Yes, some boards have more powerful power supply circuits on them so you can draw more current from their power supplies, but again that is largely irrelevant.

The one thing that you seem to be forgetting (or haven't realised) is that the microcontroller board does not have to supply all the power.

The Arduino, Pi, Teensy, chipKIT, whatever, is merely a controller. If your system needs more current it is up to you to provide that current. The Arduino etc merely controls the circuit or device that it is connected to.

It is very common to have multiple power supplies in a large project - each providing different voltages, or being used for different specific tasks within the project.

Just one thing you need to remember: Connect the grounds.