no difference. There's a misconception that brown eggs come from free range chickens and white eggs from battery chickens, and hence brown eggs are healthier, but that's not true. You can raise any breed in any condition. It has much more to do with the food the hens get, not the shell color or where they're raised.
Even free range, pasture fed hens don't give eggs that are all that different. They do tend to be higher in omega 3, etc, but there's no guarantee of that unless what they eat is carefully monitored. Poor pasture doesn't boost the egg's nutrition. The highest eggs in omega 3 are battery hens fed a special high-flaxseed diet.
I've never noticed a difference in taste, myself, between any eggs.