AB Without Diodes

Power.

The second circuit uses much more quiescent power because the ~40 uA of base current in each BJT produces ~4 mA of collector current, burning ~ 30 mW between the two BJTs.

In the first circuit, if the diodes are chosen as a good match for the BJTs, you keep the BJT's very near the edge of forward active region without actually getting them there (until they're needed) and much less quiescent power is used.

Another important point is that with the diode biasing, the circuit can be used DC coupled:

DC coupling is handy when this is used as buffer for an op-amp as it lets the buffer be in the feedback loop for all frequencies and keeps the op-amp output from running off to the rail.