My wife is a professional cellist and cello teacher, and she absolutely can tell the difference between a handmade instrument and a factory-made one. I've watched her appraise dozens of student cellos, and even though I can't hear the difference myself, I know how good an instrument is from the look on her face a few seconds into playing it. She never looks at the label or pays attention to the appearance of the body, the sound is the only thing that sets the good instruments apart for her.
As I understand it, the difference between a crafted instrument and a factory one lies in the way the creator adapts (or doesn't) to the natural grain of the wood. A handmade instrument by an expert can't be beaten by a factory process because each piece of wood resonates differently and those differences must be accounted for to get a good sound.