A better one, like you mention, is rice - again a crop with substantially worse carbon impact than chicken.
Fruits are even more complex - if you get them in season, locally and actually eat them, they are fantastic. If you buy them out of season, due to their short shelf-life you'll find they are often air shipped and have outsize waste at the retail level. Avocado is a good example here, water issues aside. In season they have a small impact, out of season they are air-shipped from South America to the rest of the world.
My point being: There are large and non-obvious differences, and they do not clearly align with traditional diets.