I get asked this a lot so thought I would put down some of reasons I like stick shaped paddles more than the Euro spoon shaped paddles.
Kayaks were developed over thousands of years along with paddles that are stick shaped. If they didn't work well the design wouldn't have survived so are worth giving a try. The main issue is that they work so differently than euro spoon blades that when people first try one and use them like spoon paddles they don't perform well so they give up. Once you learn how to use one them the way they are meant to be used they are a beautiful, elegant and efficient tools.
Spoon paddles use drag, you reach forward, dig in and pull yourself forward. The greatest resistance is at the start of the stroke when you are reaching and extended the most putting a lot of strain on you. Greenland style paddles generate lift like a plane wing. The paddle slices into the water easily at the start and ramps up resistance as it moves through the water putting a lot less stress on your body.
Spoon paddles lose all power by the time they are beside your hips while Greenland paddles generate power all the way to the stern of the kayak. You use more large muscle torso rotation and less arm muscle to push the paddle to the stern so you can paddle more efficiently without sore arms. This also makes for a longer power stroke so you use fewer stokes to cover the same distance.
Greenland paddles are never feathered so you can hold your wrists straight in their strongest position reducing fatigue of you smallest weakest joint. They also have a rectangular loom the fits your hand shape easily so a strong grip isn't needed eliminating hand fatigue that some get from gripping a round shaft.
Greenland paddles made of Cedar are light but also the heaviest part of the paddle is between your hands not out on the end of the shafts. You also keep the paddle and your hands/arms much lower when paddling and not lifting your hands, arms, paddle as much reduces fatigue.
The thin blades make it easy to extend the paddle out and hold from the end for more power when doing sweep turns, bracing, sculling, rolling, etc. The Greenland style paddles are symmetrical so no worrying about having the correct blade face direction.
They don't work as well as spoon shaped paddles for things like sprinting or whitewater paddling where digging in for quick maneuvers are important but for touring they can't be beat. Plus it's pretty easy to make your own in an afternoon that's easily as good as one you can buy.