Well, my answer is different than most. But I did some research and baby shampoo is NOT more gentle than adult shampoo. Do you know why it doesn't sting the baby's eyes? It's because there is an analgesic in the shampoo. Kind of like the stuff they put in your eyes at the eye doctor's to make your eyes numb. I'd rather be more conscientious and just make sure that no "real" soap gets in their eyes, than use the baby stuff and get soap plus numbing agents into their eyes.
So instead of using baby shampoo, I always used the same shampoos and conditioners on my girls that I use on myself. I bought some of those bath visors to keep the soap out of their eyes, as well as one of those "bath buckets" (sorry, I'm not sure what they're properly called) - it's shaped like a half-circle with rubber on the flat side, so you can rinse the baby's hair without spilling water down her face. In this way, I was able to use high-quality shampoo and my girls have always had shiny, healthy hair, without having to use baby shampoo. For my daughter with curly, dry hair, we use Aveda Dry Remedy, and for my daughter with tons of fine, straight hair, we use Fekkai Volume.
Just my two cents! I hope that helps!