Do you have a specific bird and mammal in mind?

Brain mass grows with body mass. It's so noisy that people can't decide whether it is the 2/3 or 3/4 power of body mass.* It is said that a mouse is as smart as a cow. What the cow is doing with all that gray matter, I don't know. Smart animals, like apes, dolphins, and ravens have bigger brains than the trend line, but the deviation is small, so they have smaller brains than larger animals. From this point of view, saying that birds are smart for their brain size is just saying that they are small.

* probably the right answer is 3/4 and 2/3 is just promoted by people who found 3/4 inexplicable, but Geoffrey West says that denominators of 4 are OK.