The Raft. How does it work?

If both players fill it in the same turn, is it given to the player with priority, or do both players get a card?

Both players will get one - provided that they both filled it at the same time*. It's a little confusing because the game doesn't play the floodlights animation when your opponent fills the Raft; but both players will get a 6-Drop if they fill it simultaneously.

*If one player has four unrevealed cards there, and the other player only fills it after cards are revealed, only the first player gets the free 6-drop. This is because the Raft checks for being filled before cards are revealed (Stage), then again after all cards are revealed (Reveal), then presumably one more time before turn end (Play). If it's full at any of those points on either side, it triggers and stops checking.