Ok I've had both.
Coppola gets great great great results. However, it has a bit of formaldehyde in it, which the BB does not.
The biggest difference, besides the formula, is the process. Since I had three Coppola treatments before the Brazilian Blowouts, it's hard for me to talk about the results since I couldn't compare the BB on virgin hair. Anyway, about the process.
When you get the Coppola treatment done, they wash your hair a few times with the shampoo from their line. Then they put the product in. It goes up in a shower cap, and you sit there for 20 minutes, I think. Then they blow dry it and flat iron it. This is the end of the process. You have to wait 72 hours before washing it. You are advised to keep your hair down, not wear hats, not wear sunglasses on top of your head, not tuck your hair behind your ears, etc. It's basically a huge pain. Your hair is STICK straight for three days. If it does get a bit messed up, you can flat iron the crimp out and it's fine.
With the BB, they wash it out after they flat iron and then they blow dry/flat iron again. You can wash your hair the day of. HUGE. ADVANTAGE.
Here's a pic of my natural hair a few weeks after my second coppola treatment.
here's my natural hair after my second BB (and three coppola treatments)
Def not a huge difference.
i need to go, i can add more later!