If you search here for K12/K-12/k12/k 12 and Connections/Connections Academy, you should find lots of information about both.
We've been with Connections for 7 years now. The reasons why we prefer them to K12:
* differentiation isn't SOLELY limited to acceleration. Yes, it's anemic in many ways, and you will want to offer differentiation and enrichment on your own, but hey-- that's better than nothing.
* teacher contact is MOSTLY greater than in corresponding k12 schools (from what we've seen with good friends/family in three different states)
* acceleration rules are easy and fairly straightforward in K-8, and less flexible in high school.
* how much time online... um... this varies dramatically by grade and by family, but with Connections, K-8 CAN be done with only 1-2 hr of computer time daily, no problem. A HG+ kid can easily get a days' worth of work done in just a few hours, anyway, which helps.
* Connections uses textbooks. While I may not love their choices... at least I can purchase them myself when they aren't provided. I *hate* online-only platform coursework, since the option to provide offline materials doesn't exist. This is the problem with a lot of k12's material (from what I've learned through conversations with family/friends, as noted).
It's not what I'd call "ideal."
If you have a child prone to perfectionism, this system can REALLY fuel that in a bad/multiplicative manner. I think I've detailed that elsewhere fairly liberally already, so I won't rehash it all here.