When I was a kid, I tried laundry soap. Didn't work too well. My hands were irritated from all the brushing, trying to get them clean. Then I discovered GoJo, worked OK but it was kind of yucky. Then I discovered Safety Kleen hand cleaner. Pretty good. But the shop I worked at stopped using their service. They switched to Zep which wasn't as good.
I struggled until Fast Orange came out. Good stuff.
Then I discovered Kim Care, which what they use at work. I still convinced it is the best stuff around.
Neutrogena bar soap and if necessary, a toothbrush, will get most mild dirt out. But for the nastiest, dirtiest, most ingrained dirt, Kim Care does it, without excessive srubbing..
It's my opinion, what else can I say?