When you think about current-mode or current driven, a current source has a high output impedance, and it ideally drives a circuit with a low input impedance. This will result in the maximum amount of current going from the source to the load. On the other hand, a voltage mode would be a low source impedance driving a high input impedance which results in the maximum voltage across the load.
Current-mode is therefore associated with low-impedance nodes which results in low voltages. So you need less supply headroom to maintain linear operation. But one of the fundamental rules of engineering is the no free lunch principle
and so you have to look at what you're trading for this better linearity (usually noise performance and power consumption).
Aaron