It looks to me like the first one is using Sziklai_pairs for the output stage, see:
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and the other is using Darlington pairs, see:
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Either of these should be suitable for audio output stages, though I didn't study these in detail.
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They are both right. Note that in both cases, the arrow in the emitter points down in all cases (from positive toward negative)
The first output is made of an inverter driving an inverter, with 100% voltage feedback to the first emitter, so the the pair act like a very precise follower, but with more stability issues, because of the inversion inside the loop.
The second version has output stages made of just a follower driving a follower, with no local voltage feedback, except that inherent in each follower. This produces a less DC accurate follower, but with a higher frequency response (if the transistors are the same) and the distortion is removed by overall amplifier feedback.
After checking the peak voltage capability, I usually check the gain versus current curve and pick transistors that do not require currents much above that which forces the gain down to half of its peak value. Then I check the safe operating area and overall wattage rating against the amplifier needs and heat sinks available.
The first amplifier does not specify power supply voltage rails and I don't know your load resistance. But the second one (with +-37 volt rails) requires transistors with at least something like 80 volt capability. From:
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the 100 volt rating looks like a possible.
The gain falls from a typical peak of something like 55 around 0.3 amps, but falls to about 27 at 5 amps, so that is all the peak current I would ask of these transistors. That would limit the load resistance to about 7 ohms or more.
Checking the second breakdown (safe operating area) curves, you might stay within the safe area with an 8 ohm load. But I think you are risking damage with a 4 ohm load. Lowering the supply voltages a bit helps a lot (lowers the peak current and the peak voltage across the transistor with an inductive speaker load that keeps the load current going a bit as the voltage swings back through zero, so supply voltage across the transistor while current is flowing, briefly).
So these might serve for some loads, but will not withstand much abuse, like paralleled speakers or speaker wiring shorts.
The first circuit does not detail the Vbias part of the circuit between the two output half drivers, but that bias has to see the transistor temperature, so it can compensate for the changes in base emitter drop of the hot output transistors. the second schematic shows one way to make such a bias generator, and TR13 should be thermally coupled to the output heat sink.
When one transistor is fully on, the other has the sum of both supplies across it. If the load is not pure resistance (part inductance or capacitance), there is also some current through the load as it passes through zero volts, instead of the current being instantaneously proportional to the voltage across the load. This means that it is possible that there will be almost the full sum of the two supplies across a transistor and it will still have to be conducting some current.
The two dimensions of the safe area are voltage and simultaneous current (instantaneous power). The higher the voltage across the transistor, the smaller part of the total die conducts that current, so the power gets concentrated in small hot spots. The die cannot heat sink those hot spots (and keep them below the peak allowed temperature) as well as it can spread the heat of full die heat production, so the power capability goes down and the duration of peak power goes down. Very short duration heat pulses can be soaked up by the die, itself, but cannot get out to the package fast enough. This is why the safe area chart contains several lines representing voltage and current combinations of various durations.
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