Transformers get a bad rap because of the poor quality transformer boxes that Stax built to enable a traditional speaker amp to drive electrostatic headphones. Transformers really aren't suited for large step-ups at high voltage levels. However, a purpose designed transformer based amp with a low step-up ratio can be very competitive with direct coupled designs and has some advantages of it's own. Direct coupled designs will always win the measurements "war", but may not be to everyone's sonic preference. People tend to forget that classic tube gear like McIntosh used transformers and to some ears still crushes modern solid state designs.
The key to any transformer design is the transformer itself. There are no high quality "off-the-shelf" models. I built a transformer based electrostatic amp with custom Electra-Print 1:1+1 high level phase splitting transformers. These were speced for 20Hz-30kHz (-1dB) and a 1kv swing. In order to maintain bandwidth, the primary is limited to about 3k, and a 1:2 step-up is about the realistic limit of this type of design.
Some advantages of a transformer based design are reduced parts count, more power supply design options, two stage designs equivalent to direct coupled 3 stage (transformer step-up), and perhaps most importantly, the ability to easily implement DHT's into the design. Disadvantages, besides technical measurements, are the increased size and weight of the amp, the lack of much published design information, and tthe substantial cost of the transformers.
As far as the sound of equivalent designs goes, you get the same arguements that divide the larger audio world into modern solid state "neutralists" and SET/vinyl classicists. I have a modest but well respected direct coupled solid state amp as well as a fairly ambitious transformer based tube design. I prefer the transformer design. YMMV.