I've done two major tank moves in my reef keeping career.
The first was a major disaster
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40 Gallon tank I had running for a year in my condo when we bought a new house, the major problem was that We only had two days from taking possesion of the new house and having to get out of our condo, the move was done all in one day.
Basically I kept 90% of the water and transported it along with corals and fish all mixed in the buckets and the rock dry. Saved the sand and reused without cleaning. When at the house added sand rocks and dumped in water and added fish and coral.
Within 2 days all of my coral had RTN'ed.. SPS and LPS. My fish survived but battled a major ich outbreak.
This just about had me call it quits for the hobby but I kept the tank running and just did basic maintence for 6months with fish only.
My second tank move went much better but was planned out learning from my mistakes.
I was just switching tanks (old 90G to a new built 90G) But I only saved about 50% of the water and kept it heated and circulating in garbage pails, my live stock and coral were all kept in seperate heated aerated containers. I reused sand but rinsed it really well and added 2x as much in new sand as well.
The switch took two days but allowed me time to get the tank up and running with 50% & 50% new water and gave time for the "dust" to settle overnight before I reintroduced my livestock.
If you can get the new tank up and running first that is your best bet but the other option can be done but take your time and be carefull. Bag all your fish and coral seperate when you move them in this scenario.. thats a lesson I learned the hard way .. and when reusing sand and rock give them a good rinse first
PS - if you need a hand when doing the move please feel free to drop me a line and I would be happy to help.