@Stefan Olsson, I came to STRONG right after S&S. For squats and presses, doubles feel much more natural to me than singles, probably because of my background with olympic weightlifting. That said, the STRONG DVD made my presses feel much better. I understood being tense during lifts, but zipping up tension was a new concept to me, and I loved it.
As far as weight, I don't know. My single press is about 2/3rds of my double press. I can press an 88 lb bell any day of the week, but I can only press a pair of 70's. You're still recruiting full body strength with the single press. The double just forces you to recruit a bit more.
I think because doubles tend to come after singles in the learning progression that we think doubles are more technically demanding. I don't necessarily think so. I think squats, presses, and cleans are easier to develop a feel for with a pair of kettlebells than say a snatch, clean, or get-up with a single. So I'd say don't worry about it being inappropriate to go to STRONG after S&S just because it uses a pair of kettlebells. If we were to line up all the kettlebell movements up on a timeline distributed in terms of learning difficulty, I don't think we'd a see all of single bell movements at the front the line, followed by all of the doubles. I think it would be more intermingled. Some movement patterns are easier, at least for me, to learn bilaterally than unilaterally. Thinking out loud. Hopefully it makes a little sense.