Like it or not, point-to-point leisure travel originating in the SE will constitute a massive proportion of growth in demand. This is the 'bread and butter'. And the LGW option is perfectly capable of addressing this need in a market segment which it already dominates.
Picking up Sheds point there are four airports serving as short-medium haul point to point "reliever" airports in the London sytem which can provide enough additional capacity for the next 10-20 years with further increments of development (but no new runways) - Gatwick* itself can probably do another 5-10m, Stansted 15-25m, Luton 15m and Southend can chip in a bit - so together that's circa 50mppa additional.
*Gatwick also serves as a long haul leisure point to point airport
If we can have just one new runway then the most critical and imediate task for that runway is long-haul / hub capacity - which means Heathrow.
Putting it at Gatwick will just result in a re-distribution of traffic from Stansted, Luton (and Southend) as all these basically serve the same market segment. I did hear a funny story about Gatwick Senior Mgt touring the other London airports to drum up support but using a presentation that indicated said runway would actualy take traffic from those airports!
OK once we get beyond that, in say 20 years, to the second new runway (waits for laughter to die down) then at that point it will be a much closer call between Gatwick and Heathrow because by that stage there will likely be a need for more short/medium haul point to point capacity.