The actual tread contact area will be the same at the same tire pressure, but a wider tire will have it oriented differently than a narrower one. BMW chose the taller ones for lower drag, and they also chose to use forged wheels (which are stronger) while weighing less than a standard alloy wheel. Tall/narrow is better for acceleration and stopping...wider is better for cornering. If you want better handling, buy the i3s where they've changed some things around.
Being narrower should mean you have less chance of actually rolling over something that would pierce the tire! The lower profile 20" tire/wheel setup has less cushion, so is more likely to damage the sidewall (and worst case, the wheel) than the 19". Plus, if you do drive in the colder weather or in snow, the 20" are ONLY a summer, performance tire, so are not expected to work great in the cold/snowy conditions, and the rubber compound is more geared towards traction than longevity, so the 20" tires are very likely to wear out sooner than the 19" ones.
You don't have a choice in OEM sizes except if you're looking for winter tires, where there's at least one other one than the Bridgestone...one from Nokian, their R3 is available for the i3 which is a low-rolling resistance tire compound designed as a winter tire.
2011 535i x-drive GT, 2014 i3 BEV