Both are excellent. They are also solving completely different problems, and the mismatch is expensive.
The comparison usually gets made on the wrong axis. Service, design, price per night — these differ, but not in ways that predict whether a given traveler will be happy. The useful distinction is philosophical, and it shows up in what each brand refuses to do.
Aman is built around removal. Space, silence, an almost aggressive minimalism in both architecture and interaction. The staff ratio is high but the visible presence is low. The experience is designed to make the guest feel like the only person in the building, and in some properties, briefly, they are. This is extraordinary for a certain traveler and mildly alienating for another.
Six Senses is built around participation. Wellness programming, sustainability narrative, an earnestness that Aman would never attempt. There is more to do, more to engage with, more of a stated point of view about how one ought to live. For a family, or for anyone who finds silence uncomfortable, this is often the better fit.
The practical failure mode is booking the first for a trip that wanted the second. A couple celebrating a milestone in near-total quiet is well served by Aman. The same couple traveling with two teenagers is going to spend a great deal of money on a property their children find boring, and no amount of thread count fixes that.
Neither brand is a mistake. Choosing between them on price, or on a photograph, usually is.