I do not hear any warmth in the Concerto at all and I suppose it sounds almost the same as the Classic regarding sound characteristics. Neither does it sound cold at all. They are both what I would call perfectly neutral and they have the same weight and body as the Quickstep.
I do think that the Concerto is much better with T1 (600 Ohm) than the portable Quickstep and the two amplifiers cannot be compared when using high impedance headphones. Most of my listening these days are with the T5p and with other low impedance headphones the Quickstep (15V PSU) does a very good job and I am not sure I could tell the difference between the Concerto and the Quickstep driving the T5p in a blind test.