My experience is when KUL moved from Subang (now SZB) to the new KL Intl Airport (KLIA).
The moving date was declared way in advance, I seem to remember the date was locked more than 6 months before, and a lot of airlines rescheduled their ops especially the nightstopping aircraft. Obviously Malaysia Airlines had to ferry a bunch of planes over but its a 10minute hop and done in the early hours so not much of an issue. Some of the ground equipment was ferried over earlier in the day (of the last day of Subang operations) but everything else was moved over once the last flight of the day was completed. I'm talking motorised stairs, K-loaders, belt-loaders, tractors, trolleys, dollies the works. It was quite a convoy of flat loaders. Stuff that could be driven on public roads were given temporary permits so you saw motorised steps and water/toilet trucks on the public highways!
The biggest change was moving from a host (MH) checkin environment to a homegrown common-use system which was integrated with the Baggage Handling System (BHS). The first days baggage handling was chaos with a lot of bags not making their flights.
A lot of items can't be duplicated not only in terms of equipment but also in manpower and its easier to make a clean cut and manage the problems for a 24hour period than drawing the pain over a period of weeks.