I have seen/heard differences between huge necks and skinny necks (via Warmoth ‘investigations’ and such) on video but I wouldn’t be able to identify those differences in real life. In their experiments (same guitar, same chunk of wood, same pickups, same amp, etc), the thicker neck sounded fuller, deeper, stronger, bigger.
However, the difference between Pattern and Pattern Thin seems a lot smaller than the neck differences in the Warmoth experiment. I doubt that there is a discernible difference between those two PRS necks, because it’s not like Pattern is a Tele boat neck. Because of this, I feel like you’d hear more of a difference if one neck was maple and the other mahogany (or even different kinds of Rosewood) than you would comparing Pattern Thin to Pattern on the sole basis of profile or depth of neck wood.