SYD (Kingsford Smith) is always increasing flights and still has capacity to do so. It certainly won't mean a reduction in flights to there.
As Gary said, its capacity is limited due to no further room for expansion and the overnight curfew.
SYD will always be Sydney's major international AP, however, what WSI does is open up so much more opportunity for western Sydney (population 2 million+) to travel. There will absolutely be increased demand for travel.
For example, if the bro's in Penrith want to visit family in Auckland, via Jetstar, they aren't going to travel all the way to SYD when they can catch a train a short distance Badgery's Creek.
What WSI (Western Sydney International - aka Nancy Bird-Walton) will do is initially offer competitively priced flights to SE Asia and the South Pacific/NZ, a large market from the local demographic. It will then expand from there into other markets like the Sub-Continent and China/Philippine's etc.
The long-term advantage that WSI has over SYD is that there is major room for massive expansion and the fact is has 24 hour operations.
Expansion to up to 80 million passengers a year, which SYD doesn't have the opportunity or capability.
This is why we needed a 2nd airport.
As you said in another post, freight will certainly be a huge part of the success of the initial opening.
It will take time - maybe 50 years - for this airport to reach its massive potential.
That is why it was so important to get the transport infrastructure (well, some of it) built now. That will massively help the development of Bradfield and surrounding areas.
Lastly, the most important three projects that should be in the pipeline are metro extensions to the City West Metro, from Westmead to the WSI Airport, the extension of the current WSI Metro line to Leppington and Campbelltown, and the extension of the current M1 Metro line from Tallawong to Schofields and then on to St Mary's to link with the WSI line.
Those 3 lines would connect all parts of Sydney to the new airport and were in current planning 3 years ago.
Unfortunately, they have all been cancelled as per the table above.