I use this on our All-Clad stainless. We've used barkeepers friend in the past, I would say that it works similarly if not better than barkeepers friend but I chose to buy the All-Clad branded stuff this time because it comes in a much better bottle that makes it easy to sprinkle on in reasonable quantities and reseal.
It cleans the stainless extremely well without much effort at all when using a scrubby sponge and only a little bit of product. It even cleans the discoloration off the bottom of the pan which previously I thought nothing could shine off.
One word of caution is it does leave tiny scratches as it is an abrasive cleaner, if you follow the directions and clean in circular motions around the whole circumference of the pot or pan it's less noticeable and doesn't really affect anything but you might want to exercise restraint and use it only on the interior of your pieces to keep the mirror finish looking good on the outside and clean the exterior with just soap.