Here is a really quick answer to your question I posted on here a few weeks ago:
The BKt doesn't straighten your hair anymore than the BB. Your results will depend on the formula used, how much is used on the hair, then how much heat is applied to the hair to seal in the product. The BB doesn't contain formeldahyde, but many BKTs don't contain formeldahyde either. The BB can be washed out right away, but now, many BKTs can be washed out right away too. The BB uses Amino Acids and Keratin. The BKT uses just keratin and in some cases, collegen. The BB is also more expensive. You can buy BKTs over the counter and do it yourself at home or buy online at amazaon, ebay. or folica.com. BB cannot be purchased online.
The higher the Formeldhyde concentration in your BKT the staighter your hair will become. Some BKTS don't wear off, like they say, so you have to research your brand. Your results will also depend upon your hair texture. I wanted a more drastic change, so for me, BB, wouldn't do the trick. The BB seems to be more of a frizz buster than a straightener, and doesn't last very long the more you wash your hair and the "kinkier" your hair texture.
They are both BKTs. Brazilian Blowout is a brand of the BKT like Grey Goose is a brand of Vodka. They may be made from different things and smell different but in the end it is still Vodka. It is all Marketing and branding to the Nth Degree.