From what I'm able to tell by looking at the springs on various videos (Harry's was great) and still images, it appears that the primary difference is that Touring uses a progressive front spring, vs. a linear front spring on the Sport. The actual spring rate is probably very similar once the first inch of weight transfer has occurred, but before weight transfer starts the Tour is probably a double-digit stiffness percentage lower in the front.
The advantage in comfort, as some have noted, is in the ability of the suspension to soak up bumps and heaves at the front without transmitting them with intensity to the chassis. But the opportunity cost is the speed of "settle" when you do initiate weight transfer on the way into a turn. The progressive-sprung car will more comfortable over bumps, drops and heaves in the pavement, but will be a touch slower to load up and take a "bite" in the front on corner entry. I wonder if this is what some reviewers have described as a vague front end, because of the speed of loading in the nose.
The rear springs appear to be progressive on both suspension types, with the Sport spring being slightly shorter (one fewer coil) and therefore a smaller wire diameter for a similar nominal spring rate. No idea whether there's any difference in total wheel travel, we'd need on-vehicle data and/or detailed damper specs to figure that out.
Rear spring difference from the Harry factory visit video... as you can see, both of these are progressive. Tour on the left, marked 110 N/mm rate, and the Sport on the right, marked 115 N/mm rate.