.300 Win Mag is my choice for small game- rabbits, squirrels, annoying geckos with a British accent. It does FAR less damage to the meat.
Of course, you do not shoot the critter. You shoot just above them.
Shockwave of the bullet passing over slams them into the ground, killing them instantly, no holes in the fur.
.......except for geckos, that do not HAVE fur.....