Liver tastes like the diet of the animal. Animal fed trash = disgusting liver. Animal fed clean = good liver
Livers I ate ranked worst to best:
Pig - yucky, haraam. To my defense, I'll eat anything once (no cats or dogs)
Chicken - tbh mostly yucky but I still sometimes eat it
Turkey - rare liver but if you can find it it's always better than chicken
Rabbit/hare - not my favourite because it doesn't taste too much like a liver at all
Beef - grass fed beef liver is very good, plus it's a decent size liver so you can eat one and be done with liver cravings for like 2 weeks
Donkey - pretty standard liver that's on par with beef
Horse - top notch liver, horses are smart and eat well
Veal - you're entering the territory of peak liver
Game (deer and deerlike creatures) - obviously top notch, very nice, like very high quality beef liver
Game (boar) - boar liver is superb, my 2nd favorite, boar meat in general is outstanding, boar is the player character to the disgusting domesticated pig npc. If you can kill a boar make sure to eat its liver
Lamb - cute animal with tasty liver, my favorite liver, very delicate facture and subtle taste, if you prepare it the right way (fry adequately thin stripes, then put it between buns with some caramellised echalote marmellate and some guanciale for added crispiness), it will be like these "hamburgers" NPCs eat, only actually tasty and nutritious. Also if you can, try getting the liver of a milk-fed lamb, it is basically a sheep newborn slaughtered at 3-4 weeks and never fed anything other than its mother milk. It's a liver as pure and perfect as you can get
I plan to eat the livers of many more species in the future and I doubt I can be stopped
edit: forgot some mammalian species