I would agree with those who say that you need to try one, or preferably several, to see whether there's one that you like.
Throughout the history of the 4001 / 4003, Rickenbacker have changed just about everything except the overall appearance of the bass.
They have changed the tuners, the Truss rods, the fingerboard material and its radius, the thickness and profile of the neck, the types and position of pickups, the tailpiece material and design and even the body construction; making both through neck and set neck versions with and without the walnut skunk stripe in the neck.
It's still one of the coolest looking basses regardless of which one you go for but, the weight, the comfort, the playability and the sound that they make can vary significantly.