Yes, Dead Man's Chest ends on a cliffhanger, because the Kraken pulls Jack and the Black Pearl under the sea and the surviving crew believe he is dead. Jones opens the chest and finds the heart gone, since Norrington took it, and Norrington then gives the heart and the Letters of Marque to Beckett, who now commands Jones, the Dutchman and the Kraken.
The last beat sends the crew back to Tia Dalma, where they agree to try to rescue Jack at the world's end. She introduces their guide, the resurrected Hector Barbossa, which sets up At World's End. In my opinion, this is the smartest choice in the film: Jack is the one character who cannot be pinned down, so the story answers by literally sending him to the bottom of the sea.
How does the setup work, step by step? The chain starts with the Black Spot and the debt to Jones, runs through the key won in a game of Liar's Dice, and lands on the three way duel on Isla Cruces. That duel, shot in the forests of Dominica and on White Cay in the Bahamas, is the practical set piece that decides who gets the heart: Norrington runs with it, and Beckett ends up holding it. Then Elizabeth chains Jack to the mast, because she realizes the Kraken wants only him. It is a human choice, and it gives Elizabeth a darker turn than anything she does in The Curse of the Black Pearl.
How does it compare with the other films? Compared with the first film, which is a self contained rescue story, this one trades a clean finish for a handoff. That was possible because it was shot back to back with At World's End, so the cliffhanger was a planned bridge and not a gamble on a sequel. Compare it with On Stranger Tides, which stands apart from the Jones and Beckett storyline and does not depend on this ending at all. Bill Nighy wore a motion capture suit on set for Davy Jones, and the Oscar for Best Visual Effects shows how much the film leaned on that creation to keep its villain frightening even while the heart changes hands.
It could be argued that the ending leaves too much unresolved, and a viewer who watches the sequel on its own will feel that. That being said, the three way duel sets each side up for the finish: Will ends up with the key, and the heart ends up with Beckett. If you plan to watch, keep the third film queued, and see the Pirates of the Caribbean movies in order for how the pair fit together.