* Android, when the product offers a host of mainstream computing features. I think the rationale for going with Android is: "The user already knows how to use it."
* Linux, when the product is cheaper, and has a more bare bones or restricted function set. I don't know for sure, but I think that a Linux build can be more stripped down. Little boards like Raspberry Pi and BeagleBone abound, and if nothing else, you can create a nice proof-of-concept with one of those. I've actually done this, writing my code in Python, with the expectation that the "real" programmers would turn it into something else.
I'm not in the skill areas that actually develop this stuff, so I don't know any lower level details. My job tends to be supplying the theory of operation for the actual measurement.
Both systems use SOM's (system on a module) that are typically sold with the software tools to get you started, such as a working demo OS. It is rare to see real-time stuff done on the main computer. Since you're usually talking to some sort of device hardware anyway, it's usually more convenient to put the real-time stuff on a separate microcontroller, that's got little or no interrupt overhead to deal with.