Depends on the design. You can make both do the same thing.
Usually if the control circuitry is powered from a different voltage level than that powering the motor, it will use 6 transistors. Using the two extra NPNs to turn on the PNP power transistors
Also note that you absolutely need reversed diodes across the power transistors of an h-bridge.
Without them the transistors will quickly be destroyed.
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As for the examples you have uploaded:
The 6 transistor example only allows forward, backward, and coast. While it uses more parts than the 4 transistor example, it's simpler to control using two inputs.
4 transistor example is a "Full Control" h-bridge. It allow forward and backward movement like the 6 transistor h-bridge but also allows braking. However it also requires 4 inputs.