My favorite is Lavender Palmolive, or the Lavender Lotus, which I am having a hard time finding. The last I picked up was a pink Palmolive, which smells like roses, and was hard for me to tolerate as a dish soap scent.
Blue Dawn for me is too stripping to my hands. Also I have always noticed an odor on the dish rag when I've used Dawn, as the dishrag dries out.
I cannot stand that smell, and I only notice it with Dawn products. I do keep it for other cleaning. I know it has a great reputation. But whatever about it is unique leaves an odor that just turns my stomach, almost like mildew, and it stays on my hands if I pick up that dish rag. I am talking just from drying out after one use of the dishrag, too.