Does bridging amplifiers affect their sound?
The most important consideration is : how well can each amplifier drive half the nominal impedance?

For example, one of your example circuits shows a bridged amplifier driving 8 ohms : how well does each half-bridge drive 4 ohms?

If it maintains its full output voltage into half the impedance, doubling its power from 5W (8 ohms) to 10W (4 ohms), without any increase in distortion, then the bridged amplifier will sound fine supplying 20W into 8 ohms.

But if its output doesn't double, or the distortion increases into a lower impedance, that's exactly what you'll hear in the bridged amplifier (only 3dB louder).

And if you speaker is only 4 ohms like many car audio speakers, then the question becomes, how well can each amplifier drive 2 ohms?