Advantages of jet drives are that they offer increased manouverablity (see this video:
), they can operate in significantly shallower water and there's nothing to hit below the waterline like a prop or a leg.
The downside is they are less efficient than a conventional sterndrive (by about 30%) and so require a larger engine to maintain the same horsepower. They are noisier and vibrate more as everything's inside the boat (they also take up more room as a consequence) and they are more expensive to buy and fit. Also, if you're not careful you'll suck up stones or weed and this will damage the impellor and may stop the boat in its tracks.
Mind you, how many stern-driven ribs would dare try this? -
(f/forward to 1:35).