Input impedance is higher in Common-Emitter than Common-Base?
Although in both the common base amplifier and in the common emitter amplifier (non-swamped: with a nonexistent or bypassed emitter resistor), the signal appears to be coupled to ground only across the BE diode. So intuitively, you might expect the same low impedance in both.

However, in the common base amplifier, there is a dynamic action going on which lowers the input impedance.

The  action in the common base amplifier can be understood like this. Suppose that the input AC signal swings a little bit low. This increases the \$V_{BE}\$ voltage. The collector-emitter current is very sensitive to \$V_{BE}\$ so a small increase \$V_{BE}\$ causes a large increase in the current.  But in this common base amplifier, the collector-emitter current goes through the input. So, the input pulls down the voltage slightly, and a lot more current pours out!

Since the current flowing out of the emitter reacts sensitively to the input, it means that the input stage behaves rather like a voltage source. The opposite (a current source) would not react to voltage changes at all: the same current would flow regardless of our attempts to shake the voltage this way and that.

And, of course, voltage sources are what? Low impedances!

So in summary, the common base amplifier has a kind of active voltage source behavior, according to how the collector-emitter current responds to changes in the applied input voltage, and this gives it a lower impedance than you would expect just from looking at it statically.

This behavior is absent in the common emitter, because the input interacts with the base current, not the collector emitter current. In the common emitter, we even get feedback-driven impedance raising action if we add an unbypassed emitter resistor.