There is no fixed percentage that is the "best" overall. Generally 16% or 17% layer feed strikes a happy medium.
The amount of crude protein that a hen needs each day depends upon stage of growth and production level. It is a fixed amount, not a percentage of the feed. Let's say a hen needs to take in 20 grams per day to meet growth, maintenance, and reproductive needs when it is fairly young at at peak production.
A hen generally eats to fulfill it's caloric requirements. The caloric requirement depends upon the activity level of the hen and the ambient temperature. In the winter a hen eats more, in the summer a hen eats less. Given that a hen eats more in cold weather, the prercentage of protein can down in the winter (this can be accomplished by supplementing scratch in the winter, which effectively dilutes the protein). In hot weather (above 85 F) a hen's feed intake is drastically reduced. To get the required protein into her you generally need to provide a higher protein feed and cut out any treats that will dilute the protein levels.
Since I keep a large number of hens for organic production, I see the effects of this on a daily basis. The management guide for our strain of brown layers tells me at this age and level of production they should be eating .26 lbs of feed per bird and require 19.9 grams of protein per day, so it recommends a feed of 17% crude protein. (19.9 grams protein required divided by 128 grams of feed eaten equals 16.8%).
Yet that data is generally for caged birds kept at a temperature of 78 F. We have floor raised layers and it's only 65 F in the barn. Because of the higher activity level and cooler temperatures they are actually eating .28 lbs of feed per day. I grab my calculator and and find that 19.9 grams divided by 128 gram consumption equals 15.7 %, so I order 16% feed from the feed mill.
How well does that work out for me? Pretty well actually. Since I sell eggs commercially I weigh the total egg production each day. It is surprisingly consistent from day to day. I can see day to day trends as small as a one half of one percent in egg weights. If egg weights are coming on too quickly, I reduce the amount of feed that I am feeding them each day. If egg weights start trending downward, production soon starts to drop and if taken too far the birds start to lose feathers, so I give them back some more feed. The 16% I have been feeding them had been working perfectly with just a slight reduction in the amount of feed I had been giving them. The new batch of 16% feed I received the other day must be slightly lower in actual protein so I started feeding them more, making feed available all day long. Today I noticed even with full feeding that the egg weights are starting to drop slightly. I can't feed them anymore, but I can get them to eat more by lowering the temperature in the barn by five degrees...
Capiche? If you take away anything from that just realize that the amount of protein that the birds are getting depends upon how much they are actually eating and the percentage of protein in the feed can be adjusted accordingly, a lower percentage in cold weather and higher percentage in hot weather. There is no fixed percentage that is "correct", although as I said, 16% or 17% is probably a happy medium for year round use as you can adjust other factors, such as the amount of scratch being fed.