For those on the fence, either for this vehicle or something in the future, I think the best test is to listen to a quality audio source such as a CD (not your highly compressed recording on a phone or anything over the radio) and preferably one representative of the music you enjoy. Be sure to adjust the bass output as many new vehicles are bass-heavy and really ruin anything other than modern music (and the 1812 Overture).
Realize that listening in a quite showroom with the engine off is a vastly different experience than listening with 70+dB of background/road noise.
Wattage does make a difference beyond high-volume capability. Any system is going to introduce distortion, with greater distortion as the output increases. If the standard system is close to maximum output (volume) at your regular listening level it may be distorting enough to notice. It may also lack the "headroom" to increase the volume as need by the music. All of that said, I would be surprised if the base system lacks sufficient power to efficiently drive the installed speakers without noticeable distortion at "typical" listening levels.
If the vehicle is old(er) and/or has inexpensive speakers, there are many excellent aftermarket speaker upgrades available which will have an obvious affect on sound quality. I upgraded the speakers in a 6-year-old BMW and was very happy with the improved sound from the base stereo.