Why is the output resistance of Common Collector mode low while that of Common Emitter mode is high ? I think this is true for static resistance.
One good way to measure the output resistance of a "signal source" is to load it. Now, when you load the emitter it certainly produces more emitter current but, given that some of the "extra" emitter current flows through the base and out through the emitter, you are also turning-on the transistor more. The effect of this is to make the emitter look like a fairly solid and low impedance voltage source.
Contrast this to a common emitter configuration - loading the collector does not increase base current. In fact it lowers it slightly due to the internal ohmic resistance of the emitter inside the transistor. As more collector current flows, that little bit of resistance raises the true emitter from 0V to a few milli volts higher and this in turn fractionally shuts down the base current thus slightly turning the device off.
The above is a simplistic explanation but also hints at what happens when a real (external) emitter resistor is used.