How to switch from old tank to new tank

Well I did the whole move at one time. I put the new gravel in my new tank with 3/4 load of water and let that settle out (took a day for me). Then I moved my fish and a decent portion of their water (not for the bacteria as there is none in the water column but I wanted the water they were used to and it was fairly recently added water). Then I topped things off, got the new filter running and added the old filter to the tank. I ran both filters for a week and 1/2 with testing for any ammonia and nitrite. Then after that time I removed the old filter and things were done.

I also added plants (which can help) and all the old decorations. And there were no new fish added for a month while everyone got used to the new tank.

This worked for me and all the fish survived great. Your neons are sometimes tempormental so take care with them matching temps and what not.

If you are able to get hold of a pair of ladies tights/pantyhose......clean and well rinsed, you can add the gravel into the leg and tie it off..........this will help seed the new tank too

Keeping or emptying the old tank?

If you are emptying the old tank, move fish and filter media to a bucket with heater. Remove and save as much tank water as you can in 5 gallon buckets or jugs. Put top 3/4 inch of old gravel in a shallow pan covered with tank water, then move bottom gravel to the new tank, top with new gravel. Then top with old top gravel (preserves the upper level bacteria in their usual place without mixing with lower bacteria).

Add dechlorinated tank water to about 1/3 then move live plants if any, and decorations. Fill with more water and reserved tank water, always matching temps. Near the end add fish, filters, and their water. Let heaters sit for awhile before turning on, 15 minutes?

Resist the temptation to deep clean the gravel and filters at this time. If you have no plants, maybe you could clean the bottom gravel, but try to leave the top gravel alone to preserve the bacteria.

If you can run the new filter alongside the old filter in the 10 gallon before you move that would be good, but running both on the new tank is just as good.

If the old tank will still have fish and will need its filter and gravel, then try to run both filters on the 10 first. At the minimum, take the floss or sponge or whatever you can and either stick it in the new filter or squeeze it and put the squeezings into the new filter. If the 10 has a cartridge, tear the fabric off of it and put it in the new filter, upstream of the new filter media and put a new cartridge into the old filter. The old filter has a lot of bacteria on all its surfaces, not just the floss, treat it like a living thing, keep it wet.

Be calm and quiet while doing all of this. Use 2 nets to catch fish, a big one still to catch and small one to chase. Keep a cover of some sort on the bucket, run heaters and airstones in the bucket. It won't take too long to do all of this so just keep filters wet in shallow open water.