Twenty posts, without covering a few basic points for Richard. Larger, higher-VA transformers have higher core-magnetizing currents flowing. This current flows independent of any load. But since the magnetizing currents have a 90-degree phase to the voltage, the power company doesn't directly charge us for them (there are indirect charges), and they can be said to be free, and not contributing to inefficiencies. But there are issues. First, higher magnetizing currents could mean higher I^2-R resistive power losses. Second, high-VA transformers are made with larger wire, so their I^2-R loss might actually be lower. So far it's a toss-up.
Third, until taking a close look, we don't know exactly how a given transformer was designed. It's common in low-VA designs to push the magnetization closer to core saturation, under the theory that 5-watts of core-loss heating won't be missed and won't excessively heat up the transformer. All to save a few pennies in copper cost. This little reality issue tilts the answer strongly in favor of Robert's higher-VA transformers.
Fourth, low-VA transformers also use smaller wire, which means that a high-VA type would have less loss when transforming a signal from point A to point B, especially if the signal came from a low-impedance voltage source. In other words, a high VA transformer would have less sag under load. Perhaps that's what Richard cares about when he talks about low-end frequency response?