I don't keep the substrate at all. I keep the liverock, plants, etc. even the water but not the substrate.
Too much junk in there to risk kicking a major cycle off IMO.
I use new dry substrate in the new set up and add the liverock (moved in water), etc.
I also try and preserve biological filtration in filters etc. Like if I have an old PolyFilter in the tank I don't throw it away but rather make sure it moves to the new tank, etc.
In fact if you can plan ahead you can add a sponge or polyfilter ahead of time so you have something to move lol