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.
I was reading a discussion on the VW electric...they tried performance tires on it to compare with the low-rolling resistance tires that come from the factory, and their EV range dropped by 20%. I would expect, should you choose some other tire/wheel other than OEM on the i3, that it will potentially have a similar effect. BMW worked with the tire manufacturer to come up with a tire that had the fewest compromises for this EV platform. Tall to maintain a decent footprint, and narrow to minimize drag. Change any of those factors, and you'll likely see a change in max range. Depends on what you're interested in, and what you're willing to give up for any potential performance or visual impacts.
2011 535i x-drive GT, 2014 i3 BEV
Soon (hopefully!) A 2021 X5 45e will replace the above