As you have it in the diagram, there is a 1.2V "dead" range between one transistor turning off and the other turning on. With no bias at all, each transistor is technically in Class C, as it's conduction is less than 180'
Class B would have a clean changeover between conduction of the two transistors, but without any overlap.
The higher amplifier class you go to, the more efficient, though less linear (more waveform distortion). That does not matter in some applications, but it's pretty important for audio.
See the article here:
**broken link removed**