What makes a Double bass good for Jazz or Classical?

[Sercan Say]

I'm from Turkey, here I'm working with a luthier he built several double bass, but he ordered woods cut in the shape, so he made thickness adjustments and put it all together.Now we will cut , carve woods.

What I want to know is If we want a double bass has good pizz. sound do we have to choose different woods ? Or are there any other major adjustments with wood thickness or something like that?
And same questions for Classical sound.

We recently built-one It has 5/4 body and 3/4 neck with 41,3 scale lenght, It has very full very nice bow sound but pizz. sound not that much better It has good pizz. but bow sound much more full than that.