Sorry, the way the question was worded, I just couldn't pass up the opportunity for the sarcastic answer.
I don't think anybody in the world would ever notice any difference in a live gig situation, unless it was a highly articulate bass solo with all tone controls flat or higher.
In a studio recording, you might notice some difference, but still probably not a heck of a lot. The neck being long and being parallel to the strings has much more of an impact on the tone than the body wood does, in my opinion.
So I think either one would be fine, it more comes down to the specific piece of wood rather than just the type of wood.
If I were designing the instrument myself, I would choose Swamp Ash if I wanted it to be lighter, and Northern Ash if I didn't care about weight and only cared about tone. (For example that incredible Super J five that I just sold was Northern Ash with a wenge neck, and the tone and sustain of that thing was just ridiculous, it pretty much kills every other bass out there.) But again, I would contend that it is not only the type of wood, but the specific pieces of wood. And that is luck of the draw - you don't know until you build it and find out whether or not it is a winner. Ken Smith told me he would drop the piece of wood on the floor to see what type of sound it makes, and then hold it up to his ear and tap on it all over the place to hear how consistently it resonates before he decides how to cut it and whether to use it or not. That is a level of skill that probably not too many people on this planet even have. Without that type of skill, it just comes down to "build it and see how it turns out." And even with that skill, there are still a lot more variables that go into the equation, relating to type and method of construction.
If Walnut were an option, I might choose that instead of either of the others. Speaking of which, would be nice if Sheldon offered Walnut as an option...
