My late mother in law had a slot, and there was mail all over the entry floor! It drops and slides. She did have a basket under there, but mail always missed it.

Our new house has a crazy mailbox, and I love it! It's inside a stone post, and there is a hole in the bottom of the box, so when you go away, the mail goes down the hole into the post. There is a locked door on the bottom of the post so all the mail can be retrieved when you return. When we are home, we put a piece of plywood to cover the hole.

The only advantage I can see for a slot -- nobody knows if you are not home. A slot works much better in the wall, rather than in a door, where you can have an enclosed box inside to collect the mail.