We are in almost exactly the same boat (have a 3 and 1 year old) and are currently leaning towards state but could still change our minds. It has been really interesting reading everyone else opinion.
I have been educated in both state and private (state primary and 2 private secondaries) and my husband state. Overall, my memories of school are not great in either sector. I was bullied horribly (the worst being in first private but not at all in the second) and had a lot of pressure from my parents to perform academically as they 'were not paying extortionate fees for me to get average grades'. This pressure also meant I never told them about the bullying as I was ashamed that it was happening, largely because of the pressure I had to perform. DH had a happy childhood free of academic pressure. I did end up with the better GCSE/A level grades BUT we both went to Russell Group unis, got 2:1/1st degrees, have professional qualifications and earn decent wage in stable careers.
I feel very strongly that if anyone chooses to send to private, it needs to be for the overall experience it gives the child - small class sizes, access to facilities, building confidence etc - and not solely about the grades. I don't feel it is comparable to say a child would have got the same grades at a state school as they likely wouldn't be the same person. I also don't feel it is fair to pressure a child the way I was pressured to perform as they haven't chosen to go to that school (and even if they have, they are still too young to fully understand the enormity of the impact of fees on family budget).
In terms of contacts you make - if your child is at one of the country's top independents and also a high flyer aiming for a top university and corporate role then yes, the contacts will certainly be useful. However, having a large circle of friends coming from these top schools, I can say only a couple have benefited from this. The majority have gone on to have average professional jobs where the backgrounds of colleagues are completely mixed.
In terms of the debate of education vs property, another PP has also touched on the fact that an education belongs to the child for life and they can do anything they want with it. The same can't be said for property - while I agree, it could set someone up for life, possessions and money come and go in life but the confidence and life skills from education cannot be taken away from you.
Saying that, our reason for picking state right now is that I have been really impressed with our local state primaries when visiting and cannot justify the private fees. It would take us both working full time to afford them and DH currently does long hours with me being very part time and picking up most of the childcare. For me, the children's happiness and mental health is the most important thing after my experience at school so I want to be around as much as possible; not working all hours to pay fees. From my experience, I feel a child is less likely to go to a parent when in trouble if they are not available as much or are extremely stressed. We are incredibly fortunate to be financially comfortable as we are and can afford extra curricular activities together with regular holidays if we do not have fees to pay. However, if there is the slightest doubt that either child is not happy, we will not hesitate to reconsider. Our financial circumstances may also change over the next few years and we change our minds as a result, but right now, our plan is to state educate until 18.