Wow! This is going to be a hot topic, let me be first to make a comment.
Major difference between state and independent is resources. The independents have more money, to be blunt.
So... class sizes are smaller, buildings better maintained and there is a general feeling of "polish" about the place.
In private schools, its not uncommon for reception classes to have OVER two teaching staff per class (so maybe one teacher plus an assistant plus a floating assistant) for a group of 20 kids. In state, the class might have 30 kids and one teacher.
There are two other big big differences though:
State primary schools in London have very poor sports facilities. Thats not always a problem but if you have energetic boys that might be an issue. Some of the local private schools will be exercising their boys every day.
Secondly, destination preparation.
The state schools do not really have a duty to prepare your child for independent exams.
At 11 most of the local children who are going for private schools (exceptions are those going for 13 year old entry) will sit a mass of entrance exams. Its a big ordeal and school support and preparation is important. Some state heads accept that many in their school will go down this route and be a bit flexible in terms of approach/advice.
Others can be overtly obstructive, seeing that they might be "losing" their best kids to the private sector.
If you want your child to go private eventually, and I know not everyone does, you need to have a "plan" for when and how you're going to make that leap. Mock-interviews for ten year olds to prepare them for London Day School entry are essential, where are they going to get that from?
So in a nutshell.
The holy trinity of Ravenstone, Belleville and Honeywell are great schools. And there are many many other great state schools in Wandsworth.
Do they provide fantastic educations. Yes. Will five year olds care if there are two adults singing "wheels on the bus" in class or one? Of course not.
But thats not to say that the independent schools don't bring a huge amount of value, not least if you think that route might be an option at 11.
Hope this helps