There is only one real answer - use power planes on dedicated power/ground layers.
Exact layer allocation would vary depending on how many layers you plan in total and how many and how distributed your voltage rails are.
I mean, any absolute answer, one can almost certainly assume is wrong...
It would be better to phrase as: for high speed digital, power on planes is almost certainly the right answer; potentially even multiple planes acting in parallel (when a particularly low-Z supply is needed). More likely, enough supplies will be needed (core, LV IO, 3V IO, AVDDs...) that several planes will be required in total (and more if paralleled planes are then required). Designs using even modest size BGAs, tend to be extremely limited in how much IO can be escaped and routed on 4 layers, and even 6 may be sketchy. Top-of-the-line high density designs may need dozens of layers.
In contrast, analog domains needn't use planes, as power supplies are usually low current and low dynamics. I would mainly use a plane to simplify connections (drop a via vs. having to route and bypass everywhere). You can save on some bypasses as well, with a plane. When low noise is required, use planes carefully, as you don't want to pull noise in from other areas -- a VCCA routed in from a noisy digital domain, or noisy supply* for that matter, could be disastrous. It's a compromise between plane area (reduces Z, easier to lay out) and, well, connecting everything together, noise and all.
(*Many years ago, I heard report that one then-National sync buck reg exhibited something suspiciously like drift step recovery, due to a slight dead time between low-side turn-off and high-side turn-on. The affected board had 100s-of-Msps ADCs on it, which showed occasional noise peaks which were eventually tracked to the reg's "impossible" risetime. Needless to say, noise figure was ruined until this was accommodated. I forget if it was replaced, or just synchronized.)
An RF circuit might also prefer GND all layers, to minimize crosstalk between areas; power might be routed as feed-thru connections between locally shielded sections. (Feed-thrus being "faked" with SMTs around the boundaries is close enough.)
Planes don't have to span the whole board, and since we're talking mixed signal circuits here, probably
shouldn't. Use supplies local to each domain. What counts as a "domain" depends on voltage requirement, if it needs to be switched, how much noise can be coupled around and can be tolerated, etc.
An average embedded project might have say 12 or 24V or whatever in the input / power section, a 5V domain for peripherals and interface, a 3.3V domain for MCU or VCCIO, and maybe some others as applicable (say if you have some high speed stuff or VCORE or whatever). An average design with QFP/QFN as the most dense devices, is most likely fine on 4 layers, and you should only need 6 or 8 if it's particularly high density (for which, blind, buried or HDI vias may be necessary to achieve high density, and at that point, BGAs aren't a problem either!).
Tim