Your computer doesn't "waste" electricity, power usage is on-demand. A PSU generally has 3 "rails"; a 12V (this powers most of the devices), a 5V (for peripherals/USB) and 3.3V (iirc memory modules use this). Modern PSUs are called Switched-mode power supplies that use a Switching voltage regulator which is more efficient than traditional linear regulators.
The efficiency of the PSU/transformer would be what determines if one or the other is more wasteful. Most PSUs (I would argue any PSU of quality) will have a 80 Plus rating that defines how efficiently it can convert power. I am not familiar enough with modern wall chargers to know what their testing at.. I could see the low-end wall chargers using more wasteful designs, but a high quality rapid wall charger is probably close to if not on par with a PC PSU. Hopefully someone with more knowledge of these can weigh in on this.