Is it better to repot plants with wet or dry soil?

Damp. Not soaking wet. Give the plant some ( not alot don't drench it ) water and then go get your potting supplies. This gives the plant time to soak up the water and soil won't be dripping wet when you return.

Put a little fresh soil in your new pot, water that, add your plant, finish filing the pot with new soil and tamp it down to remove air pockets, water some more. This helps reduce the shock that plants go through in the repotting process.

Sorry I dont agree. The potted plant that you are going to re pot should be moist (at all times). Unless it is a succulent. If not the plant is already under stress and wont cope with the re potting at all very well. It is true that once potted in the new soil you will still have to water it (thoroughly) and this is to remove all the air gaps around the root ball. The plant needs optimum conditions for anything like this so it can handle the stress.

Goodluck

it's better to re pot plants with dry soil because transferring a plant with a wet soil will be messy.

Do it in dry, it will make it easier. Just make sure you water them very well after to help with the shock of being moved.