I'll try again. When you bridge an amp and use it to drive a 4 ohm speaker, the amp sees a 2 ohm load. NO, the impedance of the speaker doesn't change, but the impedance load the amplifier sees driving the speaker is halved. I have had several conversations with dealers here in Phoenix, and I did talk to Jeff Rowland (the man) when he came here one weekend, specifically about this issue.
Some amps sound worse bridged, some the same, some better. I used a Parasound 1200II THX to drve a pair of Snell Sub 550THXs. Everyone who heard the system agreed the amp sounded stronger in stereo versus bridged.
Yes, a big power supply helps, but the quality of the bridging circuit counts too.
As always, listen & trust your ears....