You talk about transformers and power adapters as if they're the same but they're not.
An (oldfashioned) transformer based power adapter will be large and heavy and usually only suited for either 110 V or 240 V AC. Not both unless there is a setting for it which selects a different tap on the transformer.
Modern power adapters are quite different, much smaller and lighter in weight (for the same power rating) and can handle a wide input voltage range like 80 V to 240 V AC. These adapters are isolated switched mode power adapters and contain a very small transformer operating at a high frequency.
Your USB adapter will undoubtedly be of the second (switching) type. Does it fit in your pocket easily ? Then it's a switcher.
It depends on the design of the switched mode power adapter if it is more or less efficient at 110 V or 240 V AC. The design could be optimized for 110 V and thus be less efficient at 240 V. Or the other way around. There is no general truth here.
Maybe you think that the excess voltage when using 240 V instead of 110 V would be "burned off". Well it isn't, switched converters handle this in a more efficient way so that only a small amount of power is lost with any input voltage and any output current.
The way that such switching converters van handle such a wide input voltage range is a result of the way these converters work. The electrical energy from the input is converted into magnetic energy in the transformer and then back to electrical energy again. A transistor at the input side of the transformer switches the input power (at 100 kHz or so) and thereby determines the amount of power going into the transformer. So no more power than what is needed (at the output) is fed into the transformer ! This is a very efficient solution to control the power and thus voltage at the output.