Hi Tubby,
The TDA7052 has much more power output than the LM386. With a 6V supply and with a whopping clipped 10% distortion, the TDA7052 produces 1.2W and the LM386 produces only 325mW into an 8 ohm speaker.
Of course the TDA7052 produces more power and costs more: it is a bridged amplifier.
Advantages:
1) More power with a supply up to 6V.
2) It doesn't need a big output capacitor.
Disadvantages:
1) The TDA7052 will melt if it is driven at continuous full output into an 8 ohm speaker with a 9V supply.
2) The idle current could be as high as 20.5mA with a 6V supply if it is at its max output offset voltage of 100mV.
3) Fairly high distortion.