Both would nip pieces off of the shrimp, so they wouldn't make good tank mates.
As far as which to choose:
The first thing you should do is let a container of your tap water sit for a day or so, and then test the pH with a quality test kit such as the one API makes that is available in any pet store. Only get Platies if the pH reads as 7.0 or higher. Platies need basic water above 7.0 pH, and won't survive long in acidic water. But as long as your water is 7.0 pH or above, they are extremely hardy. But if your pH is below 7.0, then rule out the Platies and just get the Danios instead. Leopard Danios can adjust to anywhere from 6-8 pH easily. Unaerated water fresh from the tap can test falsely high, which is why I suggest letting the water sit to gas out for awhile.
The minimum tank size for Platies is 15 gallons (60 litres). They need at least 3 of their own kind, and 3 would fully stock a 15 gallon. These are also very prolific breeders, so unless you have room for fry (20 gallon tank or larger) it would be best to get all males. Females are already usually pregnant at the pet store, and can store sperm so they can give birth to multiple batches of 20-30 baby fish every few months from a single pet store mating. Platies have some lovely colors and patterns within their species, and you can have a variety of those. They are technically tropical, but can tolerate water from 65 to 75 degrees nicely.
Leopard Danios are shoaling fish. They are super active and will nip fins a bit. They need at least a 20 gallon (80 litre) aquarium minimum, and at least 8 of their own kind. They are actually a bred color variant of Danio rerio, which also comes in a wild-type striped form called the Zebra Danio and a genetically engineered brightly colored form called the Glo-fish Danio. You can mix and match within those three types to reach the total of 8. There will be some harassing and a pecking order within the group, and that's just the nature of the fish. They can also do well from 65-75 degrees.
Assuming you have the pH level and tank size for either, I would prefer the Platies because they are more peaceful and I don't like to see fish harassing or nipping each other like the Danios do. Platies are also bigger and can be seen more easily from across the room. But your kid may be able to decide themselves after seeing both at the pet store. Whichever one they're more drawn to would be good.
If your tank is 10 gallons (40 litres) it would be too small for Danios or Platies, and White Cloud Mountain Minnows would be a good bet. These are very hardy fish that need at least 6 of their own kind, which would fully stock a 10 gallon. These are true sub-tropicals, needing a temperature between 58-72 degrees. If the temperature gets above 72 degrees, they won't thrive.
If your tank is any smaller than 10 gallons, it is too small for most fish tolerant of cold water, and you would do well with just some Ghost Shrimp and perhaps a Mystery Snail, which would both do well from 65-78 degrees.