I feel the second trailer is better. Both of them are pretty... modest? Toned down? They aren't the actiony fast-paced trailers with lots of blink-and-you'll-miss-it cuts bombarding you like I'm used to seeing these days, which is refreshing and more likely than not sets the tone for the game quite well.
On to the weather trailer, I assume they artificially made the weather change so abruptly on purpose to showcase how everything looks, considering how long that thunderstorm lasts. They've put quite a bit of effort into the wind it seems, since you can see things like dust motes hang in the air once the wind dies, then fly away again once it picks up again. I'm not entirely sure how must dust would be kicked up just after a rainstorm though, that usually happens when things are pretty dry... but, that's getting into nitpicking territory. Finally, the fire from the lightning is still burning at the end fo the video =p
Turn's out OzyTheSage's speculation regarding the Shiekah Slate was more spot on that we realized.
When I made that prediction I had not seen the Sheika Slate in too much detail. After seeing a good look at it I realized it resembled a WiiU tablet more than a phone tablet. Unless the thing gets detachable mods you slide onto the sides of the thing then it was me being excited over nothing =p
EDIT: oh yes I forgot to mention... in the trailers it's pretty obvious that motion controls are in use... so unless they remove that feature for the Switch then that confirms the Switch has motion controls of some sort.