Hi Doron,
The inverter draws about 50A from a 12V battery when it has a 500W load. 41.7A for the load and the rest for heating itself. Without a load or when starting without a load, the current from the battery is probably only 2A if the transformer is good.
The gain of transistors depends on their collector current. I didn't look at the gain of the oriental 2SC1061 since if I built one I would use a local TIP31. At 1A, the min gain of a TIP31 is 25.
With a 500W load, each of the 4 output transistors for each side will divide the 41.7A so would have a collector current of about 9.7A (typical gain of 15 at 10A, and its 700mA base current is also powering the load). At 10A, the min gain of a 2N3055 is only 5!
A min 2N3055 saturates with 3V across it at 10A when it has a whopping 3.3A of base current!
Therefore the modified circuit was designed with extra gain and extra transistors so it will work with weak or strong transistors.
If all the transistors have high gain, the inverter won't draw more current. The transistors will just use less input current.
The typical input current of an LM358 opamp is only 45nA. Its max input current is only 250nA. Therefore the CD4047 Cmos oscillator IC will have nearly nothing for a load and will swing its outputs very close to 12V and ground. The LM358 current-limits its output at about 15mA, so the pre-driver transistors get plenty of base current.
You can multiply the current gains of the stages using min-spec transistors if you want. Start calculating current at the output and work your way forward.
Just remember that the darlington connected transistors add their base current to the load. ;D