Active DI boxes have amplification stages in them, and whenever you have amplification, the design itself becomes a very integral part of the sound. Some active DI boxes like the Countryman Type 85 FET based DI, adds a sort of pleasing compression and coloration to passive instrument level signal. I spoke to a seasoned engineer a while back about purchasing one, and he said that he had known quite a few guitar and bass players who ended up purchasing one to use in their live rig ever since plugging their instrument into one while working with him. There are other designs which seek to provide the cleanest, spankiest sound with as little coloration as possible, these are typically your passive DI's. Cheap chinese DI boxes, it doesn't matter whether they are passive or active, they are going to sound like junk.