BoBII is probably the most accurate single player simulation of the battle you will find. With the BoBDG updates you will have the accurate markings on every aircraft, of every squadron (on their correct airfields) on every day of the battle, practically. It has a dynamic campaign where you can take oversight of the airwar, so you can win or loose the battle. If you don't want that level of management and just want squadron level activity, you can do that too. It is also the only, let me repeat that the ONLY sim that will give you massive air raids on the scale of the battle on a modest computer without bringing it to a smoking halt. The bad news is that it is OLD and looks it.
CoD is ok. Very much improved with the atag patches and more computer intensive. The un-modded single player campaign is crap. If you expect to have a big fight over London, you'd better have a very beefy system. The on line component is pretty good, but don't buy into a lot of the atag hype. Visually, it's very beautiful but it comes with a price.