A hint: Get off the runway as quickly as you can. There is almost certainly a bigger plane on short finals behind you!
Oh wait. you are not flying there as pilot, are you? In that case, from a passenger's perspective: If the 27 runways are used, you get better views on the RHS of the plane (Parliament, Big Ben, Whitehall, Buckingham Palace, Hyde Park, Millenium Wheel, Albert Hall, Imperial College, Natural History Museum, etc.)
If the 09 runways are used, I think you can see some castle on the LHS, but you won't fly above central London so the views are not that spectacular anyway....