What is the practical difference between using an FTDI breakout board and an FTDI cable?
If you have a cable without auto-reset (or a older board) you need to hit the reset button before uploading the new sketch.
It will depend on the cable what voltage they support, sparkfun for instance has some that claims can do both. And this is from sparkfun's page

These have 5V VCC, and 3.3V I/O. The 5V Vcc output shouldn't be a problem unless this cable is being used to power a sensitive circuit such as a sensor.
There are pros and cons to the FTDI Cable vs the FTDI Basic. The FTDI Basic has great LED indicators, but requires a Mini-B cable. The FTDI Cable is well protected against the elements, but is large and cannot be embedded into a project as easily. The FTDI Basic uses DTR to cause a hardware reset where the FTDI cable uses the RTS signal.