I have both the large Veneta and original Ball, and love them both. I think the Veneta is slouchier, but the Ball isn't what I'd describe as "stiff." For me, the Veneta will *wrap* around the body and therefore its profile from the side can appear a bit less wide than it is lying flat. The Ball's outside pockets, seams, etc. keep it from wrapping around your body. But it doesn't "stick out" to my eye, and on my Ball the handle is super soft and flexible, so the bag's volume swings easily toward your back, if you know what I mean.
I think the Ball is really user-friendly; the outside pockets are awesome. The Ball does seem a teeny bit more casual than the Veneta, to me, but that may be a function of the colors I have. Two additional considerations: because of its structure, the piping on the Ball can get worn, so if you really care about keeping things looking "new" that may be a factor. And I find the Veneta has more capacity. Good luck with your decision!