Hey OP,
Well, maybe nothing. We can talk some theory though.
When we imagine how things change from say, an undersized power supply to an oversized power supply the practical difference would be described as reduced output impedance.
The output impedance of an amp is a combination of many factors, including the number of output stages, amp topology (zero feedback vs. feedback) and the power supply sizing relative to the load.
With a purely resistive 8 Ohm load it is relatively easy to design an adequate power supply that ensures the amplifier performs up to it’s specified output, with a flat frequency response.
When impedances drop, and reactances rises is where things get more interesting and, generally speaking, a larger power supply will support the output stage and keep it "stiffer." That is, the amplifier performs equally well at all frequencies up to rated output.
In other words, along with the right amplifier circuitry, a low impedance power supply makes sure you get consistent performance regardless of load. As your power supply gets smaller, the amp becomes more sensitive to the speaker load and the output will stop being flat and will start to track the speaker impedance.
So, all kind of depends on your speaker load, volume, speaker efficiency, etc. as to whether or not you’d hear any difference at all.