Your circuit is the same but better written and with a filter capacitor(c3) and an RC filter (C1, R1). Since we have never used these circuits it will be hard to tell their efficiency. If you can share the inpout voltage/current and output voltage current and the what kind of a speaker you are using.
Simple is not always better. The circuit with the filters is more advised and more efficient. In engineering you can not afford to make that 1 mistake which blows up the device, thats why you put more, even if does work in 95% of the cases without it.