I found this article on stringemprium.com
Here it is:
Even to this day, upright basses are made using gamba outlines, with either carved or flat backs and there are violin form (outlines), with violin corners, made still in either flat or carved back models.
Is there any shape or style that is better? There are some musical (tonal) thoughts of why one might be better and there are reasons of practicality. When compared to violin or even cello making, carving a bass back is very strenuous and time consuming work. Whenever basses are made whether on a private one per order, or mass produced, basses with a carved back were always more money. This is true today and true throughout history. (Also, working and carving maple is much harder because it is much denser wood.) Making a flat backed upright bass is much quicker and cheaper.
Over time, carved back basses tend to show much less cracking. With a carved back bass, the back is more "elastic" and is able to accommodate the climate and seasonal changes much better than a flat backed bass. Also, in flat back basses, the braces used to support the back over time can peel away and actually shrink or expand in different direction than the rest of the back. This can sometimes be problematic. Some basses over time, are more prone to this because the wood used for braces are too temperamental with the seasonal change. Sometimes we just change out the braces with new ( dry seasoned) wood and this usually solves the whole issue.
Playing and sound. While there are no 2 basses the same, if one were able to compare a flat back model to the very same make (but a carved back), there might be a small difference in the way the bass responds. The flat backed bass tends to respond with a sharper, quicker attack, while the carved back bass will still have good attack, but tend to also have a little more depth to it. This of course is a huge generality! Both types of basses work and can sound great, but they have to be set up and treated according to individual requirements of that particular, one bass and player.
