I've spent some time on the 675. I thought it was meh for me. Nothing wrong with it, it just didn't inspire me. I will say that if you're not used to riding twins, you'll feel the smoothness of the 3 pot a bit more familiar. In terms of power, that's easy, the 959 would probably crush the 675 in race mode on a track but most of us don't live on tracks. I don't think the clunky nature of twins make them great around town traffic bikes. That has improved with this super Q engine but it still likes to be over 4000 rpm.
Ride them both again if you can and which ever one suits your size and riding style go with. Both are great bikes. The Ducati will be more raw, it'll be faster and you'll get a TON of attention on it from just about everyone. The 675 will be smoother, cooler (temp in traffic) and more well behaved at anything under "going to jail" speeds. I don't use my bike for anything other than play so the roughness of it is something I adore. It's also not my first Ducati so I'm well adjusted to the behavior of twins, they're not for everyone I can promise you. Both are excellent options, the choice is between something that is more focused, raw and has character in abundance vs the 675's more livable character for mixed riding.
Finally I'll say that in the looks department, the Ducati is clearly the winner.
When you rode the 959 what mode was it in? I recently saw a review online and it turns out the guy was riding in WET mode. It makes a huge difference.
