Output power of standard Class E inverter = 0.58*Vi2/Rload
Output power of standard H bridge inverter with series LC network = 0.8*Vi2/Rload
H bridge topology has 1.4 times more output power capability for the same input voltage and same load resistor than the Class E inverter. Besides that, the H bridge's transistor has to block a maximum voltage of "Vi" while the Class E Inverter's transistor has to block a maximum voltage of 3.5*Vi (for e.g. 60 V input, the transistor has to block 210 V !!!). This is the main reason that the Class E inverter is not used in high power applications, but the H bridge is.
The conclusion is this one:
Class E --> high efficiency, high frequency, low power => useful in biomedical applications
H bridge --> high power, lower frequency => high power applications