I love Skills! Like you say, they've got a great culture, and a comparable mission. There are definitely some advantages to having a "judged" event, compared to a head-to-head style competition, as you point out, but I still find the latter more fun and motivating.
I came across
this promo video from SkillsCanada. It definitely hits the same emotional cords as FIRST. I hope I'll catch a competition one day.