IMO doing it slow is better for the corals, but that’s if you have time and the extra equipment to do this.
New tank VS holding tank = same problem the bio load changes and both will cycle one way or a another.
Now if you have the time and equipment, a holding tank would be good. This would hold your corals safely while you are rearranging and setting up your rock work and adding new sand.
I have done it both ways and had no problems. I have a lot of sps, lps zoes, and large fish. Now that not to say I have lost things in the past on my first move and I have moved over 100+ tanks. This is a hobby for me and I am not trying to step on any ones feet. I have done stupid things but I have learned what to do and what not to do. My best advice to you is
1 put your coral in bucks or holding tank in side the house where the temp steady.
2 don’t disturb the sand bed in your old tank big NO NO.
3 empty all you water to the lowest point you can before you move your base rock. that way you are not disturbing your sand bed and contaminating your water.
2 the last bit of water at the bottom of your old tank do not reuse.
There might be other ways to moving a tank. But this is the general guideline I use and I have had no problems. I hope this helps