There is a big difference from a 4001 to a 4003. I started with a 1968 4001 and that was my main bass for 30 years, it had a weak 6.7k ohm toaster neck pickup, and a 4k ohm bridge pickup, and it had the .0047 capacitor the was basically a high pass filter that removed the low end from the already weak and trebly bridge pickup. Even with those issues that bass worked great in a blues band, when properly equalized and using a big old school bass and and bass cab. The toaster pickup is a 6 pole guitar pickup, and the horseshoe pickup is a lap steel pickup. These pickups were not voiced for a grunty bass tone. Also the 4001 had 250k ohm volume pots and 500k ohm tone pots with single coil pickups. The 4003 is a different animal. The pickups are wound to more like 11k ohms and the pots and caps vary but overall the 4003 is a thicker and fatter sounding bass. I have a 4004 that has been converted into a 5 string and it has single coils. When I solo or favor the neck pickup the low end is immense, while still having a treble bite.