I have only ever eaten farmed rabbit in restaurants when we holidayed in France annd Malta, almost 30 years ago. Had I not ordered it especially, I would have found it indistinguishable from free range chicken thighs or drumsticks, not a hint of gameyness.
Since moving to Otago, I am often given wild rabbit that friends shoot that I skin and butcher myself. I always soak them overnight in brine to draw out any blood and that also helps to tenderise the meat.
I have never found the meat to taste gamey, the rabbit is usually cooked on a low and slow heat, having been marinated in wine or vinegar before cooking. The simplest dish that I prepare is simply slow cooked rabbit in white wine, bay leaf, lots of garlic, black pepper with a dash of oyster sauce.
The meat is stripped off the bones and served with pasta.
Another favourite recipe is similar to the Silver Palate chicken Marbella but simpler - white wine, vinegar, prunes, thyme, brown sugar, bay leaves and long slow braise.
Even wild rabbits have a very mild flavour, unlike hare which tastes like liver to me.
I urge you to try cooking rabbit - any chicken recipe works well with rabbit, just be prepared to extend the cooking time.