All power bricks use transformers of some kind - these reduce the voltage and provide an isolation barrier between the mains voltage and the output.
The difference is in how the transformer is connected. The traditional method has been to use an iron core transformer connected to 50-60 Hz mains voltage, then rectify and smooth the output, and then optionally regulate the output.
The more modern way (called a switching supply) is to use an inverter circuit to convert the mains voltage from 50-60 Hz to 20-50 kHz, usually the inverter has some form of control circuit in it to control the output. This voltage then goes to a transformer, and is then rectified and smoothed. The inverter takes care of regulation.
The advantage of the switching supply is that the bulky, expensive and heavy transformer can be replaced with a tiny, cheap and light transformer.
Efficiency of a power supply is highly dependent on design and quality of manufacture. Traditional mains frequency transformer power bricks often used the worst possible transformers, with every possible corner cut to minimize the cost of the expensive iron, copper and shipping. These transformers often had losses that dwarfed the actual energy usage of the load. A number of years ago I measured and catalogued the losses in dozens of home transformers that I had collected. The results suggested that "off-load" idle power consumption, more often than not, exceeded the actual rated load. In other words, a PSU capable of 5W output, would often take 7-8 W idle wastage when plugged into mains power, but disconnected from its load. The efficiency of the transformers was otherwise dire, and for small transformers it was unsual for the efficiency to be above 60%. The worst I saw was a "6W" transformer that consumed 8W at no-load, and 22 W at 6W load. For something like a cell phone charger that would be "on load" for maybe 2 hours per day - it was entirely typical for the amount of energy wasted by the transformer to be 15x as much as the energy used by the actual phone, if it was left plugged in when unused.
Despite the simplicity of some of these traditional power supplies, reliability was not as good as you might think - especially for regulated supplies. The incredible inefficiency resulted in extremely high temperatures, which severely degraded any electronic components in the PSU. I had some old computer external PSUs which I had to replace on an annual basis because they burned out, precisely because of this inefficiency. I eventually bit the bullet and bought a much bigger industrial supply and modified it - it outlasted the computer.
Switch mode supplies tend to be more efficient because the manufacturers are less likely to cut costs in the transformer, given that the costs of a switching transformer are much smaller than those a traditional transformer. And even if the manufacturer does cheap out on the transformer, most switching control chips, will automatically sense no-load conditions and go into a deep-sleep mode, regardless of how cheap the overall design.
There's nothing that inherently makes a switcher more efficient that a simple transformer - just that making a high efficiency transformer requires lots of high-quality materials (or expensive manufacturing processes - e.g. winding copper onto a toroidal core, which is very labor intensive and requires very expensive machinery compared to winding copper wire on a two-part iron core).
If someone really, really wants high efficiency (e.g. very powerful transformers for power plants which are extremely difficult to cool because of their size - very high volume for their surface area - extreme efficiency, in the region of 99.7%, is necessary to prevent the transformer from getting incinerated) then they can have it. It's just very expensive.