PWM Controled H-Bridge Amplifier

I'm using PWM to generate audio using the Arduino. I'm using the one transistor amplifier documented here:

Even through sound is quite audiable it's used outdoor and people mentioned it would be nice to be louder. I've read about h-bridges as pwm amplifer and realized with the single transistor the speaker only get 0 to +12v. With a h-bridge I still only get 0 to +12v but since the current direct can be changed I can get the speaker to move in both directions.

Would this make the speaker loud or am I complete off bases here.

Thanks John