Save contacts to phone or Samsung Cloud? I am unsure which is the better option.

Phone because that's what it's made for.

Cloud because if I want to move phones, they come too.

Where should I compartmentalize my contacts?
If the choice is only between these two, I'd say go with Samsung cloud. Or if you can choose another, choose Google Contacts or Outlook Contacts. These because it will be easier to sync them to a non-Samsung device if you decide to jump the ship in the future.

A cloud backup is recommended because:


They will still sync to the device and remain on it just like phone contacts do.
If you lose your phone or it suddenly stops working, your important contacts will still be available on the cloud and you can download them to your new phone.
Contacts are easier to access on multiple devices. Say if you switch phone or keep 2 phones. And you can also get your contacts on your PC.


One disadvantage of cloud is that if you (or your child) mistakenly deletes the contacts from one device, then the deletion will get synced to other devices as well and you may lose important contacts. 

You might want to save your Contacts locally on the phone if you have privacy concerns and you do not trust the cloud with your contacts. Do remember to manually back them them up periodically by exporting them and transferring to your PC.