But, about a 1/2" shorter sidewall ht. on the tire.
Yes, the sidewall is very close to 1/2" shorter on each side or 1" overall. This allows for the 1" larger wheel diameter with no change in the tire OD.
Usually a shorter sidewall will result in less sidewall flexing for "tighter" performance and a "stiffer" ride. There is also a higher risk of rim damage from road hazards. Additionally, the unsprung weight of the bigger wheel/shorter sidewall is usually less, improving performance. I'm not sure how much the weight difference really matters with our dynamic magnetic suspension. I would expect a bias is built into the software tuning for the stock unsprung weight.
There is a styling component as well. Some prefer the look of the larger wheel.
Another thing to consider is tire availability for a given tire size. Not all models of tires are available in all sizes. There may a tire that fits your needs available in a 20" diameter that is not in a 19", or the otherway around.
Up to a point, it's all a matter of personal preference and where you want the balance of comfort, performance and styling to be on your own car. The further you vary from stock the higher the risk going out of the engineered "safe zone".