I got the same groupon ad.
As a veteran of Speed Ring (the previous business at K1 Speed's location) and Lemans Karting, I called Lemans and then K1, I spoke with employees of both places that have experience in both facilities and got their impressions on the difference between the two businesses. Here's what I got from them:
1. Karts are similar in performance with K1's cars having quicker acceleration but lower top speed, and K1's cars are quiet since they're electric. The quiet cars make the whole facility quieter.
2. K1's track surface has more grip than Lemans indoor, but less than Lemans outdoor tracks.
3. K1 has shorter sessions and you have to swap cars more frequently since the cars are electric.
4. K1's facility has a larger indoor track, but no outdoor track. The combined indoor/outdoor at Lemans is larger, but you don't always drive the combined track at Lemans.
5. K1's facility is newer, nicer, flashier (brand new).
6. K1 is geared more toward the general public and less toward enthusiasts. Lemans is generally geared toward the general public too, but they are enthusiasts themselves and are very friendly to people who are there more for the driving practice, as long as you don't act like a Jackalope and ram the regular people out of your way.
7. Overall, they are similar and you could have fun at either place.
I didn't ask about the kid/age aspect, but it makes sense that K1 allows kids in the karts earlier than Lemans does. If I recall, I think my son had to be 13 or 14 before he could drive at Lemans. He also had to attend a special training session on a Saturday before he could drive. K1 can get younger kids in the junior karts with less restriction and hassle. So K1 looks like its much more kid friendly.
Since I go to the karts only for the opportunity to work on my driving and keep my skills up, I think I'll probably keep going to Lemans, but everyone has different priorities and K1 might be better depending on what you're looking for.
Either way, its probably worth a visit to K1 to check it out and make your own comparison.