In most mic's, a transformer is an integral part of (and mostly specifically designed for) the individual amplifier. Thus, sonic properties are unlikely to be attributable to a transformer alone. The most important component for sonics is still the capsule, though. Many modern mic's come with different capsule designs than the classic ones. Also, current manufacturers utilizing classic electronic designs will use individual capsule designs, etc. etc. - So in order not to compare apples to pears, you would have to A/B different circuit topologies but use the same capsule (and, to be precise, also the same head, grille construction etc.). This has been discussed here at length a few years ago...
The presence of a transformer mostly denotes a classic tube or solid state amplifier, usually with one or two active stages, little or no negative feedback in the first stage, resulting in low order distortion products that rise proportionally with i/p level. Here, the transformer may contribute frequency-dependent distortion (usually at the bottom end), but the general sonic properties will be set by the topology of the whole circuit.
In modern designs, the transformer is no longer needed for impedance matching of the output, which instead is provided by a multitude of transistors (sometimes close to a discrete op-amp), involving a good deal of NFB in order to realize high headroom and minimize distortion. The i/p stage being designed in a similar fashion, the amplifier will impose virtually no distortion before it eventually goes into clipping.
A few personal examples:
- in many situations, I get equal results with both a Neuman UM57 and their M582 head-amp with a UM70 head. Both mics use an M7 capsule and the EC92 tube, but they differ in transformer and (somewhat) in circuit design.
- I once A/B'd a KM84 with a KM54c using a KK64/84 capsule (i.e. both mics sharing the same capsule, but one being a FET the other a tube design) for recording acoustic guitar at ca. 1m distance. There was no significant difference.
- the sonic differences between KM8x and KM18x (meaning, transformer based vs transformerless complex electronics) series mostly result from a revised capsule design in the KM18x which affects the high end
Lastly, an example from AKG's C414 mics from the 80's/90's generation: Two C414 versions, one xformerless (the TL II), one xformer based (the ULS), sharing the exact same electronics. Still, you can't compare them with regard to the xformer, since both mics have different capsules...
So you really have to be aware of what exactly you're comparing.