Barkeeper's Friend smells worse, but seems to work slightly faster. I always wear gloves when using it because it makes my skin itch something fierce.
Bon Ami takes a little more elbow grease and comes in a way cuter can. Also costs less (about $2 less).

Bon Ami uses natural ingredients like baking soda and limestone. Read about it here: http://www.bonami.com/index.php/about_bon_ami/environmental_stewardship/

The main ingredient in Bar Keeper's Friend is oxalic acid. It's definitely stronger.

They're different brands of household cleaner that essentially do the same thing -- though Bon Ami seems to be gentler.