For high frequency RF amps (Fc> 100 MHZ), the aerial is normally connected by a bit of Coaxial cable that matches the aerials impedance -in the range 50-75 ohms. In this case you still want a voltage amplifier, but if the device is matched to the low impedance, then extra gain or linearity can be got at no no expense, such as using a grounded base transistor.
Current amps are unusual, I have never seen one because if you need a high current output, then normally you need a reasonable voltage to drive the current into the load, so you have a power amplifier.
Frank