Capabilities are one of those concepts that's a bit like FP or RISC. It sounds elegant but in the real world experience is mixed, so it's rare for a system to rely on it purely. Most real security systems today are built on semi-static permissions granted to domains defined by some third party identity system. Capabilities do get used, but mostly in the sandbox context and mostly as a detail.
So I think Dan is not quite correct that mobile platforms use capabilities. Users assign permissions to specific apps semi-statically there. The lowest levels of the OS may use a small set of capabilities as part of the implementation, but granted permissions are not generally easy to send around to other apps.
"Is this app allowed to read your contacts?"