What is the difference between single cut and double cut basses?

The difference between the two designs is mainly the length of the part of the neck that can freely flex and vibrate. The part of the neck that is attached to the body does not vibrate because of the thickness of the body and neck together. This area is too stiff to flex and vibrate.
A singlecut design has a shorter neck that can move and vibrate with the string vibration. Therefore it absorbs different frequencies. This results in a quicker and more direct sound and improved articulation with piano like voicing.
A double cut design has a longer neck that can move and vibrate and this results in more punch and a snappier tone. Traditional bolt on construction adds even more to the attack/punch.
Bolt on double cut design is the best choice if you are looking for a punchy rock or vintage sound (Fender) and old fashioned slap tones.
Singlecut design is better if you need great tone definition and is perfect for chordal playing, jazz, fusion, progressive rock etc.
But with choosing the right wood combination for fingerboard and neck we can increase or decrease the described sound features of each design.