We bartered for 5 gallons of BioPac dish soap several years ago. It is fine, and has lasted us an age.
I wanted one of those foaming soap dispensers for the kitchen. I had a coupon, so I bought a Dawn Direct Foam container. Of course, I just used the soap inside until it was emptied and I could put the BioPac in it. I didn't like it very much, it smelled terrible.
A couple days later, I was washing out a Ziploc bag, and I was like, "Wow, this was easier than normal. Cut right through the greasiness inside the bag. Is it because I used a brand new dishcloth..." then I looked up at the smirking Dawn container. It's true. Dawn really gets the grease.
The Direct Foam smells like it belongs on a janitorial cart, though. I have a couple of big bottles of regular blue Dawn stockpiled, and when you dilute it way down and put it in the Direct Foam container, it smells fine.