IMPO:All things being 100% equal and in a perfect world,
The bolt on will have a faster, "snappier", more articulate attack and will be tonally "neutral". Some will consider this neutrality "bright"
The set neck will have a slightly more sluggish response due to the glue in the joint hindering the transfer of vibration slightly, and will have attenuated highs compared to the bolt on.
A neckthru will have a strong low midrange spike which will not increase sustain but will give that impression psychoacoustically. Also mildly attenuated highs (notably less than a set neck, though), and the response will be pretty much halfway between the bolt on and the set neck as a result of the larger surface area of the body wing/neck joint reducing the effects of the glue joint itself. The faster response and "amped" mids are a direct result of the neck going all the way through as one piece, causing the vibrations to hit the bridge (response improvement) and butt end of the guitar (midrance accentuation) before they spread to the wings.
These differences will be both audible and and in feel, and will be noticed. But they will not be immense as some make it out to be, but more in the direction of an extreme pickup swap or a bridge swap from their total impact. Again, audible and tangible, but not necessarily a "make or break" factor. A change of body wood or neck would have significantly more impact.
In pure theory, if truly 100% identical and built correctly, the bolt on will actually have just minimally more sustain because of the glue´s dampening effect present in both the set neck and the neckthru. In practice and our more than slightly flawed world: all 3 suck /rule just as much as each other