Mixed Signal PCB, 2 or 4 Layer?
first allow me to clearly state my answer. A four layer board will give better performance. The difference is not stark for all boards, but the four layer board will allow you to route signal, power, and ground, directly over each other in a larger variety of ways. Keeping ground directly under the power plane will reduce crosstalk for close proximity lines and reduce noise by allowing overall better routing choices. With four layers, single point ground is an achievable feat without also cutting the ground plane in two. Essentially, if the two layer solution requires cutting across the ground plane, then you are creating two ground planes connected by two points. This allows a current loop, causing noise, and this can be exacerbated by temperature differentials, nearby electronics, etc. I am not sure as to the use case of this device, but the temperature, nearby EMI, and operating frequencies will all play in. If this is a semi-high speed design, then a four layer will definitely save the integrity of those signal lines. A lot of this comes down to how much resolution you need from those ADCs. If you truly need 16 bits, then I would say a 5% performance increase from a four layer board is worth it.

A great reference which I pull my design guidelines from is...
http://www.ti.com/lit/an/szza009/szza009.pdf

Cheers