Something which I don't think has been mentioned yet is around wind direction. Sydney generally experiences two strong wind directions - southerly and westerly. The westerly winds are particularly prevalent (and strong) in the August-October period. The runway alignment for Badgerys Creek (southwest-northeast - 05/23) will allow the runway to be used for the vast majority of wind conditions. Kingsford Smith on the other hand has two runways aligned north-south (16/34) and one east-west (07/25). This configuration means when the strong westerlies come through, the crosswind component makes 16/34 unusable for many aircraft, reduces operations down to one runway, and causes delays.
Personally, as has been suggested by a few other posters, I would like to see Badgerys Creek be the major airport for Sydney, with Kingsford Smith serving an LGA style role with some domestic flights and business aviation. 16L/34R could be removed from service (and 16R/34L could be shortened significantly to a similar length as 07/25). Looking at the long term development plan for Badgerys Creek, I can't see Kingsford Smith remaining as the primary airport.
One other big impact the development of Badgerys Creek will have is on flight training. The site is smack bang in the middle of the training area used by Bankstown and Camden (I used to practice engine failures with students all the time in the vicinity of the site). Camden will be able to still do training to the south, but it will be interesting to see what will become of flying training at Bankstown.
Actually southerlies at SYD aren't really that common, if anything the prevailing winds would be north westerlies. The strong southerly winds are more associated with storms and strong cool changes and then there are the spring westerlies blowing gales. But, the predominant ops are on the 34's with the norwesters and in summer the north easterly sea breezes.
The directions chosen for Badgerys Creek are interesting as being fairly local, I've found the winds won't be much different to SYD. There will be a fair bit of cross wind ops, but in general the north westerlies don't usually get to strong, so ops shouldn't be affected too much. I would guess 23 in winter and 05 in summer would be the expected ops.