I found an article a few years back on how to host a chickens tasting party. Basically you invite a bunch of friend over and serve them chicken. You prepare the chicken with recipes that are simple and bring out the flavor, but don't cover the natural flavor with an over abundance of spices. You have to prepare your guess as judges by explaining that Gourmet Restaurants and the food industry in general put a lot into being able to offer the best quality and that their feedback would be very valuable in advancing that cause. Then you serve everyone a few breeds of chicken and let them evaluate the texture, flavor, etc.
We have only done this in our home once. I know we served a 3 month old Marans pullet and think the other meat was a store bought chicken. We didn't do the formal feed back on that meal, but I saw that members of the Austin Backyard Meet-up Group gathered and did a chicken tasting activity 2 years back, so some of this is going on.
I personal have sampled Breda Gueldre, Cream Legbar, Silkie, Marans, and Basque.
My favorite all around birds is the Marans. It have a very dark rich meat. I have heard that some French food critics list the Marans as their favorite, but in France the have usually see the Bresse or the Crevecoeur listed as the favorite. I have not tasted either of them.
The Silkie....The meat of the silkie is very tough, so it can't be used in your standard chicken recipies. It requires a lot of tenderizers. We prepared ours with a signature recipie from an Asian Restaurant in the USA that uses Coke-a-cola for the tenderizer and it was the most flavorful chicken I have ever tasted. It is a Black Meat/Black Bone Chicken like the Ayam Cerami and the Silkie is a delicancy in Asia. We had our Silkie the week my second Daughter was born. The Asians say the black bone chicken has healing power that aid in postpadom recovery. So...this is the darkest meat I have ever eaten with the most flavor, but the carcass was small and the meat tough, which is why I would list it as a good all around winner for meat.
The Basque... This is much lighter meat that the Marans. It is a light exotic flavor. I prefer to use this meat at our house for herb recipes. It just doesn't seem to be as good a fit with BBQ, sweet, or spicy recipes as other breeds that we have. As Maggie's Dad stated the Basque are still being established in the USA. We got our fist Basque the spring on 2012. These seam to have gone through a bottle neck with their imports. Our Basque are smaller birds than our Marans and less prolific layers. Breeders in Canada that have had large breeding programs for 6-8 year report much better utilities than what my flock has. I feel this breed will reach the same quality as the flocks in Canada that our US stock came from, but it will take several years. The Basque is the friendliest breed of chickens I own. When the State Tester came to do P/T testing this spring my Basque were all free ranging. This would have been a problem with any other breed that I have because I it would have had to chase the flock all over the pasture to get subjects for testing. With the Basque I just walked into the pasture whistled and they all came running to me. I scooped up a hen and handed her to the tester and the cockerel didn't have any problem with people handling his hens. Not even when she was pricked to draw blood and let out a squwk. I then scooped up the next hen for testing and the flock just waited by our feet begging for attention.
The Legbar... This is the breed that taste the most like what I am used to calling chicken. The Brown Leghorn and Barred Plymouth rock are the main breeds in its makeup. I read in the March 2014 edition of Exibition Poultry Magazine that the Pullam Coach companies purchased exclusively Brown Leghorn Cockerels for all the Fryers served in their Dinning Cars up to about 1928 (year?). The Leghorn usually isn't looked to as a meat bird, but the meat is quite good. I like the Legbar meat better than the Basque, but I would not keep it as a meat bird because I can get twice as much meat with a Marans or Basque in the same amount of coop space.
Some other things to consider...1) Harvest age 2) fattening 3) Caponizing
1) Since I raise chicken for eggs and processing culls is just seen as a necessary part of flock management I am a big fan of Poussin. This is also know as spring chicken or Corinish Game Hens (even if no Cornish or Game fowl in used). They are feed gains and dairy for a month and harvested when they are 1-1-1/2 lbs. This is the succulent meat of baby chickens. They don't have the flavor of slow grown birds harvested after 16 weeks but are like fat pigeons and a delicacy in France. I like them because it is less feed that is spent on raising culls to 16 weeks and the meat is really soft.
2) Many of the breeds listed on this thread (i.e. Bresse, Sussex, etc.). are traditionally dairy fattened before processing. This process greatly increased the quality and yield of the meat. Some feeds like peas and corn give the meat a course texture. Fattening gives the meat a fine texture and marble fat through the meat making it gourmet quality. Some breeds fatten better than others. Breeds that fatten well should have a large frame and broad breasts. The age of fattening is also important. Some meat breeds grow quickly to 14 weeks, then actually lose weight for a period as they continue to mature, so you have to know when each breed is best to harvest.
3) Capons are fixed cockerels. They grow larger than intact males and the meat is softer and has more fat. Capons traditionally are harvested at about 10 months. When finished this is the best quality chicken available. I haven't had capon and my wife won't let me fix any of our birds, but Basque and Bresse are both breeds that are traditionally caponized and harvested in December for Christmas feasts. I have head people compare the Capon meat to pork because it is higher quality that what most people would think of as chicken.
So... breed is one part of the equation, but how you raise and finish the birds is a much bigger part of getting the best quality meat. The breed you choose for 4-5 week old Poussin may not be the same one you choose or 16 week slow grown birds and a 3rd breed may be the idea for 10 month old capons. You also might choose a different breed if fatten birds than if you don't. There is a reason that their are 100's of breed of chickens.