I think I've been fortunate in the past. We once got a kitten from a neighbour (who's son was my friend), but I'm not sure how old the he (the kitten) was. Maybe 6 weeks, maybe 12 weeks. Regardless, I think he grew up as well-adjusted as he did because his mom, who was an indoor-outdoor cat (that's how she got pregnant in the first place), would wander down 2 houses, to our back door, and would cry until we brought Grizzly out. Then she'd groom him and love on him and even try to take him back to her house before we'd stop her. So in a way, Grizzly still got his socialization lessons from mom.
We got Willow 8 years later when Grizzly disappeared (he, too, was an indoor-outdoor cat, and was eventually caught in someone's cat trap and disappeared). Willow was 6 weeks old, and our first indoor-only cat, and she grew up...odd... She's skittish, nervous, anxious, flies off the handle real easily, etc. Fortunately she does have good bite inhibition (thank goodness for small favours, eh?). We got Buffy 2 years later, when Buffy was a 4 week old orphan. Her mom and litter came to the vet hospital (I think they were strays), but they were all sick and all but Buffy ended up dying. The day after Buffy lost her family, she came to our place (screaming like a banshee, might I add). She was still on milk formula, but I praise the heavens that we had Willow. You might not think that this poorly-socialized, territorial, SCARY cat would be a good role model for Buffy, but surprisingly she was. She doted on Buffy, groomed her and taught her and loved her, and Buffy grew up well-adjusted. Granted, Buffy "inherited" some of Willow's odd quirks, and she's a stubborn little knucklehead, but she loves people and attention and is extremely intelligent. And, as a plus, having Buffy just happened to really mellow out Willow. She's now calmer and less territorial (though she doesn't hesitate to kick ass when she thinks Buffy's being threatened by my dog or a stranger, lol).
Personally, I think 12 week kittens (and puppies) are cuter than 6 week olds. So you get the kitten twice as old than if you'd gotten her at 6 weeks, but you'd get the 12 week old either way and she won't be 6 weeks old forever. Before you know it, a month has gone by and she's getting older and older, and you don't even remember what it was like when she was 6 weeks old. 6 weeks or 12 weeks, you get your kitty in her kitten stage for MONTHS, six weeks extra or six weeks less means nothing as a result. And by waiting just a month longer, you get a more well-adjusted, friendly, loving kitty that won't make you grow more grey hairs over the next few years, lol