Not sure where he got 40%. However, it can be broken down as follows:
1ph 480V you are using a 3 wire system. 3ph 480V you are using a 4 wire system. Basic math, you use 33% more wire in a 3ph system than you would in a 1ph system.
Delivered power in a 1ph system, in basic physics, P=IV.
Delivered power in a 3ph system, in basic physics, P=1.73*IV.
You get 73% more delivered power in a 3PH system.
Hence, for 33% more wire, you get 73% more delivered power using a 3PH system. So, maybe your friend did 73-33 = 40%, which isn't exactly correct but sure whatever.
3Ph becomes more efficient as your loads get increasingly larger. It was first invented for power distribution (in the Gigawatts). I wouldn't get too caught up over a 1kW load. 15kW and up, start looking into it.