After years of trying a boatload of basses, amps, effects and cabs, not to mention the serious $$ wasted "researching", I have found my tone. However, I have to utilize 3 pedals; MS-60b, DHA VT1-bass drive DI and a B7k.
MS-60 = tuner, comp & eq
DHA-VT1 = traditional real tube overdrive and compression
B7k = adds a touch of modern distortion and mojo
So, back to the OP's question.......seriously tough call. Probably the DHA because of the natural tube OD, compression, DI and it has a headphone output.