Are there any problems in your 60 gallon that you don't want in your new tank (aiptasia, problem algae, etc.)?
If there are, reusing your old sand will almost certainly transmit them to your new tank.
I also personally would rather just start over with new stuff. You'll never get all the crud that's built up in a sand-bed out through rinsing it. It may never be a problem for you, but it's one more potential source of one.
The argument for keeping it is that there might be things in there you don't want to lose, but unless you personally went to the ocean and collected a bunch of sand from the bottom of a healthy reef then flew it home in a heated, oxygenated vessel, there is nothing in your current sand bed that won't be rapidly repopulated just through the normal activities of setting up a tank.
All those worms and pods that do so well in our tanks are the beneficial equivalent of aiptasia - they're organisms that through an accident of evolution developed a set of traits that enabled them to do inordinately well in aquariums. They can survive trips across the world on damp rocks, reproduce in a way that is compatible with protein skimmers and filter socks, are either not eaten by the fish we commonly keep or reproduce fast enough for it to not matter, and can handle swings in temperature and parameters that would kill the things you actually paid for. There are 10,000 species of polychaete worm, and yet you'll only find the same 5 or 6 in every marine aquarium on the planet. I bet if you were to do a detailed survey of the micro-fauna of 1000 mature tanks on 5 different continents, you'd find a very consistent community of animals, and you'd find it whether the tank owner ever did anything to encourage it or not.