My Due has a 5V line on it that will provide a 5V Vcc capability if you need it.
You will need to check that devices that you connect to the Due are OK with the 3V3 signals that it provides and also that it does NOT push 5V into the Due inputs. Even with inputs to the Due there are simple ways to protect the pins.
However, many devices will work with the 3V3 signals that the Due puts out (it is all a matter of the voltages that the devices needs to decide if the signal is "0" or "1") and this is generally OK. Some devices have level shifters on them to allow them to work with both the 5V and 3V3 signals (in both directions) - for example I have 1.8 inch TFT display that works happily with both voltages, depending on the voltage you feed it.
As for your servos, they typically take signals from the Uno or Due and so you would need to check on the data sheets to see what the minimum input voltages are that they need. You may well find that they require 12V or something in which case they will already have the level shifters or drivers in them, or you can add some very cheap MOSFETs in yourself.
I would not be afraid of the voltage differences - just careful.