Having handled several custom ukes and production ("classical" in the OP), my personal opinion is that there is most definitely a difference in sound quality provide that the custom builder is one who has a reputation of building great sounding ukes.
Of the custom builders ukes that I have played, I have tried at most a couple of ukes they built because unless you live in close proximity of of the builder, it's simply unrealistic to have tried too many instrument from said builder. However, I've pretty much only ordered custom ukes from builders who have a stellar and impeccable reputation when it comes to player instruments. In just about all cases in my experience, the custom built instrument not only have great sound, but also have a great feel. That is, the instrument feels alive when I'm playing it. I'm not completely certain what gives off that "vibe", but probably because the custom builder was able to fine tune the ukulele through bracing and thickness tuning on the soundboard. For me this "vibe" differentiates custom built ukes from production ukes more so than the sound.
Don't get me wrong. I don't think a custom instrument automatically sound better than a production instrument. And to me there is a big difference between a high quality sound versus something that sounds good to a particular person (a uke can have a high quality sound that doesn't necessarily sound great to everyone. For example, I think a National resonator uke have a high quality sound, but I don't personally enjoy it more than a traditional ukulele's sound). But I'm pretty confident, through my personal experiences, that a custom built instrument from a highly reputable builder will be superior to a production instrument most, if not all, of the time.