Good question. Very good question. Above my head also somewhat.
The lamp itself is resistive and as Mayhem mentions, unless the resistive load is sufficient (normally 75w) for the dimmers to work with, it won't without a ghost loading somewhere around to make them function on most electronic dimmers but not all types of dimmers especially variable resistance types. A household
dimmer being a variable resistance type for the most part should work given it's quality or range. At lower rates, that dimmer also will not be sufficient to incandess the lamp without going to at least almost full first. Were that load on a
SCR dimmer or of sufficient load on a resistance dimmer be it from other fixtures on the dimmer of sufficient load or it's own lamp wattage than it would be effective no matter the dimmer type or transformer. (Chopping of the sinewave verses reducing the voltage.)
On the other hand, the transformer is a inductive load as classically stated in that it induces a lag time on the lights effected by the dimmer and further disrupts phase
harmonics in much a similar way to the dimmer itself which is for all intensive purposes a transformer. It is also possible that this lag, phase harmonic shift and other variables on the load side of your electronic dimmer can be harmful to it by way of extra heating onto it and other reasons. It's also possible your dimmers will conpensate for this especially if not as high of a resistive loading is in effect. Such inductive loading is evidenced by if you send a low voltage lamp to full on a light board and it's going to take a moment or three longer than a line voltage lamp to go to full by way of the transformer. The lag time is inductive loading and also measured by some amount of heat or loss in the transformer. Max out the loading in wattage on a dimmer without accounting for transformer effects on it and it's very likely you will not blow it out but overheat it.
A final factor is in the low voltage lamp itself. A common low voltage lamp requires full voltage for optimum operation of the halogen effect gas within it. Otherwise, that gas when operated at temperatures less than design will attack the pinch seal of the lamp itself an not prolong it's life. (The other than noble gasses in the lamp prolonging normal filament life will seek out and eat away at the cooler parts of the lamp thus the pinch seal.) Some question of the effects of series operation of low voltage lamps on dimmers but not a transformer, or stage lighting lamps such as in a strip light, but for the most part, your 12v lamp when dimmed will not act as per halogen lamps. They will operate at the expected halogen effect color temperature the lamp is designed for as per a normal halogen lamp, but for the most part only have the life of a incandescent lamp operated as it were over it's rated voltage. A low voltage lamp on a dimmer frequently will not be a very good long term option for stage lighting use. For a specific show sure, but other than that is not much to work with in efficiency. The life will be greatly reduced.
The volume in line voltage verses low voltage power is normally sufficient, no matter if it's voltage chopping or voltage dimming that the halogen effect on the lamp's filament is not having such problems with dimming.