Bunnies do not only have different visual traits, there are also non-visual traits that greatly affect the bunny's quality.
From the looks of the bunny to the different boosting traits. These are all determined by the genes of the bunny upon minting.
This affects how your bunny looks.
This reduces the time required to breed new bunnies. In general, it takes 30 days to breed a new bunny. However if your bunny has a breed booster trait it can potentially take half that time (15 days) to breed a new bunny.
This increases the amount of $PILL generated a day while staking. In general, bunnies produce 100 $PILL a day. However, if your bunny has a $PILL boost trait it can potentially generate 2 times that amount (200 $PILL) a day.
NOTE: This trait only affects bred bunnies and not the First Generation bunnies.
This affects the success rate of breeding new bunnies. As Fade Away Bunnies are degenerative in nature, they tend to be suicidal. The more suicidal they are the less likelihood that the breeding will succeed.