The state school sounds good, not average.
All three of mine have been/are in state schools with Ofsteds ranging from Satisfactory to Outstanding. Ofsted is just a snapshot of some of the things that the inspectors look at over one specific period - it's really only part of the picture. My dc's primary school moved from Satisfactory to Outstanding while my dc were attending, even though it didn't suddenly become a different school overnight!
The feel and atmosphere of the school is much more important, and all the things that you list as pros for the state school are the things we value in the schools my dc are at (two now at secondary, one still at primary).
Another advantage that you don't list is that the benefits of a more mixed environment extend to the fact that you don't get anything like the same level of parental pushiness, anxiety and competitiveness, which is a huge relief. This is I think distinct from 'work ethic' - at private schools there will be much more focus on achieving particular (not necessarily interesting) academic benchmarks, and many parents will be eagerly adding to this pressure at home, sometimes with tutors. At a state school there will be a much wider ability range, and not all parents will be able or willing to micromanage their dc's education to the same level. But that's not nec a disadvantage, and may even be a plus as the dc have a bit more space to develop their own interests.
The mix of backgrounds, abilities and interests in the classes also means that there is much less peer pressure in terms of who is best at schoolwork, and who has the latest gadgets or went on the smartest holiday. My dc are all fairly robust and relaxed about the fact that some people have more than them or find work easier, whereas other people have less, whereas the experience of my brother's dc (who are at a school similar to the ones you mention) is that there's much more competitive-based nastiness of the "oh, can't you do that, you're a baby", or "oh you only went to Yorkshire for your holidays, we went to St Barts" variety.
Overall, I would say my dc are probably a bit more robust and laid-back than their privately-educated cousins. Academically they are if anything slightly ahead, though they get far less homework and don't have such neat handwriting. If your social circle consists of lots of private-school parents, then get your flak jacket ready and tune your ears to bypass mode, because your decision will inevitably be unsettling for people who are paying £12K a year for something not ultimately that different from what you're getting for free. Some people are so focussed on private being the only option that they sound positively surprised to hear that children have actual lessons in state schools, or don't get beaten up on a regular basis. 
You do need to keep your nerve a bit, and remember that the school has a wider set of priorities than just fine-tuning the abilities of a very narrowly-selected range of kids. And in fairness there are some schools that do not do justice to all dc. But if there is a real, longer-term problem you will spot it, and there's plenty of time to move schools later on (lots of movement at 7+ and beyond). As long as your dc are happy and learning, and you keep a bit of an eye on what's going on, there's no reason why they shouldn't get an education that is as good, probably more quirky and fun and definitely more diverse than anything you could get by shelling out lots of money.
Welcome on board. 