When dealing with a single feedpoint, working with impedances (and a series formulation of R+Xj) is traditional - it maps well into VSWR, etc.
However, when working with multiple feedpoints, or coupled antennas, sometimes admittances work better. Most method of moments modeling tools (e.g. NEC) build an admittance matrix. So when you have an NT card in NEC, you specify the network parameters in Y parameters. And excitation is specified as voltages - that is, the goal in a NEC type model is to solve for I given Y and V. The currents in the segments are then what is used to compute the radiated and near fields. This is the inverse of an impedance formulation, which would solve for V, given Z and I.
Then, once you've solved the system, one can convert the admittances into Z (or S, for that matter).
Another case where parallel formulations are useful is when you're looking at a unmatched antenna like an AM car radio - The antenna is very short, very reactive and mostly a capacitance. It's feeding a system that is a high input R with a shunt C (stray capacitance and feedline C) - You can use a Thevenin model of the antenna as a Voltage source and a series Z, feeding the parallel combination of Ramp and Ccoax+Camp. This forms a voltage divider and forms the basis of sensitivity calculations. Here, the voltage would typically be the E field * length of antenna.
