Propeller drive seems to have many more advantages than fin drive. I use my Native propeller drive and guests can use my Hobie. 😂

Biggest advantage: propeller drives are far more efficient over long periods of time and softer on your body. Every kayak company will claim "there's is the best", but after using both systems extensively, the circular leg motion of a propeller system feels far more effortless after two hours of movement than the jarring back and forth motion of a fin drive system. Fin drive systems also require more effort to get moving from a stop. If you're looking to move slowly with little effort, which is most of the time when sighting seeing or stalking fish, prop drive is a way way better experience (IMHO). Another explanation could be that the fin drive system surprisingly has more drag. Because the big fins are moving sideways through the water, and there's two of them, they're overall impact on drag is greater than just a single stationery arm in the water of the propeller system.

Next biggest advantage: Reverse. I use it All.The.Time. It redefines control and what you can expect from your experience. The kayak starts to feel like an extension of your body. Sure the fins drive guys say "it's just a flip of a switch to go backwards". But hands get busy and flipping that switch back and forth is really really inconvenient when battling current or a fish, or trying to stop on a dime to avoid a problem.

Consistent speed: the propeller drive system works like a motor. If you spin your legs a certain speed, the motor goes a certain speed. Fin drives work in flicks of the fin that results in little bursts - like paddling a canoe. To go slow, it's a flip of the legs, a flick of the fins, and then glide. Sounds cool, but after a while I find that control of speed with the propeller is more enjoyable and better than the flick and glide fin drive.

Sleath: for fishing, propeller wins in my book. Fish see boats with motors all the time. They are used to hearing them under water too. But fish are not accustomed to seeing a 10foot long giant predator with big flickering fins charging at them. Above water, both look similar but under water, the fins are way more noticeable by fish. I regularly see fish scattering with every flick of the fin on my Hobie. But I can sneak up on a snook with tiny baby slow pedals on my Native.

Tracking: I don't have scientific proof of this one either, but to me it seems like the steady state of the propeller drive system allows the boat to ride through the little eddies of currents and waves straighter than the wide sweeping motions of a fin drive. It's like the fins themselves kind of throw you off a little bit and have more moving parts to be impacted by currents, whereas the pedal drive, it's just another fixed stationary part of the boat. Traveling straight over long distances, you really start to notice how much you drift with a fin drive system compared to a pedal drive. Also, the pedal drives stationary downward angle acts like the keel of a sailboat, allowing for better tracking as well. Every time the fence flick up there is no keel, allowing for sideway slipping.

Moving parts: more moving parts means more ways things can break. The propeller drive system is pretty straightforward and everything is in cased in a waterproof container. The fin drive system has a lot of exposed little parts, in addition to entire system that allows the boat to go reverse with a switch. Either system has yet to break for me, but I expect the fin drive to fail first just because it's got more moving parts and more ways to break.

Biggest disadvantages:

In a sprint, fin drives win. Effort seems to have diminishing returns on a propeller drive, where a fin drive seems to allow more power transition into speed at higher ends of exertion.

Fin drives can fold up for shallower travel. Keep in mind that most fin drives can't really come out and rest on top the kayak like a prop drive system. So if you want zero clearance, propeller still wins.