As with all woods, there is a LOT of overlapping. By way of example, we have built Swamp Ash basses that weigh close to 10 pounds and Northern Ash basses that weigh less than 10 pounds...much of the difference depends on the actual weight and density of the given pieces of wood in question.
Designing completely custom instruments is always a series of trade-offs. In the case of Richard's 33" scale Imperial, he really wanted Vinny to make the instrument as compact and lightweight as possible. The weight and size were the prime drivers of the design. So, 33" scale was used, the lightest piece of Swamp Ash in the shop at the time for the body, the body was carved to be slightly undersized to minimize weight, etc. As a compact-sized bass guitar the instrument excels. It plays and sounds really great, for what it is and was emant to be.
Contrasting this to Richard's first Imperial, however, which was a 34" scale and weighs 11 pounds (fairly heavy Northern Ash with an Olive Top) and you get two very different instruments. First off, Richard just never got really comfortable with the way the 33" scale length responded under his fingers. For him, it just never felt like home.
From a tone perspective and having heard both of these basses, I would say that the biggest difference that I personally noticed was the incredible presence in the low-end of the heavier, longer-scaled instrument coupled with an almost ringing-piano like, highly nuanced quality to the low register notes. Funny, the 33" scale bass sounds killer in its own right, but when compared directly to the tone that Richard had in his head from living with the other bass for so many years, they really do sound very, very different. The 33" scale has a more compact tone. Quicker sounding with a more definitive attack and end to each note but with less deep bass...
Of course Northern Ash can go way too far in the other direction. My first real bass was a 13+ pound early 1980's Fender P-Bass and that thing was fairly dead sounding...
So, what are the basic sonic differences between northern ash and swamp ash? My last Imperial had northern (I believe) and it was quite heavy and flat sounding.