Question: Which is better, feather or plastic vanes?
Answer: What are you trying to start a fight? All kidding aside, ask bowhunters that question and you will likely get as many reasons to use one or the other as the number of hunters you ask.
The only real answer is, "it depends."
The advantages of feathers are (at least in part) as follows. Feathers are lighter than vanes, thereby making your arrows slightly faster. Feathers are more flexible, thereby reducing arrow wobble from any incidental contact the fletching might have with an arrow rest. I have heard that feathers are quieter (but my half deaf ears wouldn't be able to make that judgment). Feathers come in left wing, or right wing packages - the natural bend of the feather. If you are using feathers and your fletching tool has a helical (a bend or twist) then your feathers wing must match the helical (either right or left).
The advantages of vanes are (at least in part) as follows: Vanes are more stable in wet weather environments and will provide more consistent flight in all weather (although feathers will probably provide slightly better flight in dry weather). Vanes can be placed on arrows without regard to left or right wing that must be considered with feathers. If you are fletching arrows for multiple family members, with different helical needs, vanes might be more practical Vanes are slightly heavier than feathers thereby adding weight to an arrow and hence adding kinetic energy.
Storage of arrows will impact the back end of arrows as well. If arrows are stored in a case where the fletching or vanes are protected from being squashed, kewl. If however, you are guilty of leaving your arrows in a shooting quiver - like I am, then fletching will be damaged quicker than vanes.
Ok, so what is the answer? Well... the weight difference is almost negligible and can be safely discounted in most cases. The real concern should center around likely weather conditions and arrow clearance. If I knew that I would be hunting in both wet and dry weather, I would probably opt for a more consistent vane. If I were hunting in the arid west, with little likelihood of rain, fletching might be a better choice. If the arrow is coming out of the bow with significant contact with either the bow (in the case of a recurve or stickbow) I would definitely go with feathers. You should be able to avoid most vane contact with a bow with properly tuned arrow rest, so vanes should not hurt you there.
There, now that I have confused you completely I pass the question back to you: Which is better, feather or plastic vanes?