Bear in mind the waiting list for the state school may not be a date linear list. They will most likely move people up and down the list according to their oversubscription criteria. If distance is one of those criteria if you are moving within yards of the school you may jump to top of the list. If you are some distance away you may find you never get to the top of the list as others keep moving closer so in reality it is never going to be a choice. We have done things the other way round, moved from an excellent Independent to an outstanding State, she starts in September so still to find out how it goes but at the current point in time it feels like the best route for us. If the fees are easy for you then it is more about the choices you have and not the financial side which actually sometimes makes it a harder decision.
Honey's Mum - I agree with PettswooodFiona that the waiting list movements may not be very straight forward. I know people who moved and had to wait for a place at their preferred school for 18 months, while others, at a different school, got theirs within a few weeks. You can only get a place in a state school when someone else in your DD's age group moves away and leaves the school which is why the school can't tell you how long it will take.
If staying on at a current school is not a sensible option given your new location, your choice for September might be forced by the fact that the outstanding state school place is simply not available for your DD. There is also a possibility that soon after she has started in a private school, the state school place will suddenly become available - would you then withdraw your DD from the private school or let her stay on? An outstanding state school is a very good option if you can get it, but I think it may be worth looking for additional alternatives just in case, so that you have more choices.